algebra-real-functions se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
306 questions tagged with algebra-real-functions.
If (f(x)=x-2-1) and (g(x)=x-1), what is the factorized form of ((f-g)(x))?
A. (x(x-1))
((f-g)(x)=x-2-1-(x-1)=x-2-x=x(x-1))। subtraction में signs सही रखें। / ((f-g)(x)=x-2-1-(x-1)=x-2-x=x(x-1)). Keep the signs correct in subtraction.
Login to save your score, XP, coins and progress.
If (f(x)=x+1) and (g(x)=x-2+1), what is the degree of ((f+g)(x))?
A. (2)
((f+g)(x)=x-2+x+2), जिसकी highest power (2) है। polynomial की degree highest exponent से मिलती है। / ((f+g)(x)=x-2+x+2), whose highest power is (2). The degree of a polynomial is given by its highest exponent.
Login to save your score, XP, coins and progress.
If (f(x)=x-2-5x+6) and (g(x)=x-3), what is (\left\(\frac{f}{g}\right\)(2))?
A. (0)
(f(2)=0) और (g(2)=-1), इसलिए quotient (0) है। denominator non-zero हो तो numerator (0) allowed है। / (f(2)=0) and (g(2)=-1), so the quotient is (0). A zero numerator is allowed when the denominator is non-zero.
Login to save your score, XP, coins and progress.
If (f(x)=2x-2) and (g(x)=3x-2), what is ((5f-2g)(x))?
A. \(4x^2\)
((5f-2g)(x)=5\(2x^2\)-2\(3x^2\)=10x-2-6x-2=4x-2)। like terms को अंत में combine करें। / ((5f-2g)(x)=5\(2x^2\)-2\(3x^2\)=10x-2-6x-2=4x-2). Combine like terms at the end.
Login to save your score, XP, coins and progress.
If (f(x)=\frac{1}{x-2-1}) and (g(x)=x+2), which values are excluded from the domain of ((f+g)(x))?
A. (x=-1) और (x=1)(x=-1) and (x=1)
(x-2-1=(x-1)(x+1)), इसलिए denominator zero (x=1) और (x=-1) पर होता है। domain में denominator zero values हटती हैं। / (x-2-1=(x-1)(x+1)), so the denominator is zero at (x=1) and (x=-1). Values making the denominator zero are excluded from the domain.
Login to save your score, XP, coins and progress.
If (f(x)=x-1) and (g(x)=x+1), which pair is correct for ((f+g)(x)) and ((f-g)(x))?
A. (2x,\ -2)
((f+g)(x)=2x) और ((f-g)(x)=(x-1)-(x+1)=-2)। plus और minus operations अलग-अलग करें। / ((f+g)(x)=2x) and ((f-g)(x)=(x-1)-(x+1)=-2). Perform plus and minus operations separately.
Login to save your score, XP, coins and progress.
If (f(x)=\sqrt{x-4}) and (g(x)=\sqrt{x+1}), what is the domain of ((fg)(x))?
A. \([4,\infty\))
\(\sqrt{x-4}\) के लिए \(x\geq 4\) और \(\sqrt{x+1}\) के लिए \(x\geq -1\)। intersection \([4,\infty\)) है। / For \(\sqrt{x-4}\), \(x\geq 4\), and for \(\sqrt{x+1}\), \(x\geq -1\). The intersection is \([4,\infty\)).
Login to save your score, XP, coins and progress.
If (f(x)=x-2+1) and (g(x)=x-2-3), what is ((f-g)(5))?
A. (4)
((f-g)(x)=\(x^2+1\)-\(x^2-3\)=4), इसलिए (x=5) पर भी value (4) है। पहले simplify करने से calculation कम होती है। / ((f-g)(x)=\(x^2+1\)-\(x^2-3\)=4), so at (x=5) the value is also (4). Simplifying first reduces calculation.
Login to save your score, XP, coins and progress.
If (f(x)=x-2) and (g(x)=2x), what is the minimum value of ((f+g)(x))?
A. (-1)
((f+g)(x)=x-2+2x=(x+1)2-1), इसलिए minimum value (-1) है। complete square से quadratic का minimum आसानी से मिलता है। / ((f+g)(x)=x-2+2x=(x+1)2-1), so the minimum value is (-1). Completing the square helps find the minimum of a quadratic.
Login to save your score, XP, coins and progress.
If (f(x)=\frac{x}{x+2}) and (g(x)=\frac{3}{x-5}), what is the domain of ((fg)(x))?
A. \(\mathbb{R}-{-2,5}\)
दोनों denominators (x+2) और (x-5) non-zero होने चाहिए। इसलिए \(x\neq -2\) और \(x\neq 5\)। / Both denominators (x+2) and (x-5) must be non-zero. Therefore, \(x\neq -2\) and \(x\neq 5\).
Login to save your score, XP, coins and progress.
If (f(x)=x-2-4x+4) and (g(x)=x-2), what is the value of ((fg)(x)) at (x=2)?
A. (0)
(f(2)=0) और (g(2)=0), इसलिए ((fg)(2)=0\cdot0=0)। product में कोई factor zero हो तो product zero होता है। / (f(2)=0) and (g(2)=0), so ((fg)(2)=0\cdot0=0). If any factor is zero, the product is zero.
Login to save your score, XP, coins and progress.
If (f(x)=2x+1) and (g(x)=x-4), what is the value of (x) for ((f+g)(x)=0)?
A. (1)
((f+g)(x)=3x-3), इसलिए (3x-3=0) से (x=1)। पहले sum बनाएं, फिर equation solve करें। / ((f+g)(x)=3x-3), so (3x-3=0) gives (x=1). First form the sum, then solve the equation.
Login to save your score, XP, coins and progress.
If (f(x)=x-2+5x+6) and (g(x)=x+2), what is the simplified form of (\left\(\frac{f}{g}\right\)(x))?
A. \(x+3,\ x\neq -2\)
(x-2+5x+6=(x+2)(x+3)), इसलिए quotient (x+3) है, पर \(x\neq -2\)। factorization के साथ restriction लिखना जरूरी है। / (x-2+5x+6=(x+2)(x+3)), so the quotient is (x+3), but \(x\neq -2\). Write the restriction along with the factorization.
Login to save your score, XP, coins and progress.
If (f(x)=x+3) and (g(x)=2x-6), what is ((fg)(0))?
A. (-18)
(f(0)=3) और (g(0)=-6), इसलिए ((fg)(0)=3\cdot(-6)=-18)। sign multiplication में गलती न करें। / (f(0)=3) and (g(0)=-6), so ((fg)(0)=3\cdot(-6)=-18). Do not make a sign error in multiplication.
Login to save your score, XP, coins and progress.
If (f(x)=x-3) and (g(x)=x), what is the factorized form of ((f-g)(x))?
A. (x(x-1)(x+1))
((f-g)(x)=x-3-x=x\(x^2-1\)=x(x-1)(x+1))। पहले common factor निकालना आसान रहता है। / ((f-g)(x)=x-3-x=x\(x^2-1\)=x(x-1)(x+1)). Taking the common factor first makes it easier.
Login to save your score, XP, coins and progress.
If (f(x)=\frac{1}{x}) and (g(x)=x), what is the domain of ((f+g)(x))?
A. \(\mathbb{R}-{0}\)
\(\frac{1}{x}\) में (x=0) पर denominator शून्य हो जाता है। इसलिए sum का domain \(\mathbb{R}-{0}\) है। / In \(\frac{1}{x}\), the denominator becomes zero at (x=0). Therefore, the domain of the sum is \(\mathbb{R}-{0}\).
Login to save your score, XP, coins and progress.
If (f(x)=x-2+2) and (g(x)=4x), how can ((f+g)(x)) be written in complete square form?
A. ((x+2)2-2)
((f+g)(x)=x-2+4x+2=(x+2)2-2)। complete square में आधे coefficient का square जोड़कर घटाते हैं। / ((f+g)(x)=x-2+4x+2=(x+2)2-2). In completing the square, add and subtract the square of half the coefficient.
Login to save your score, XP, coins and progress.
If (f(x)=\sqrt{x}) and (g(x)=x-2), what is the domain of ((fg)(x))?
A. \([0,\infty\))
\(\sqrt{x}\) के लिए \(x\geq 0\) चाहिए और (g(x)) सभी real (x) पर defined है। इसलिए product का domain \([0,\infty\)) है। / \(\sqrt{x}\) needs \(x\geq 0\), and (g(x)) is defined for all real (x). Therefore, the product domain is \([0,\infty\)).
Login to save your score, XP, coins and progress.
If (f(x)=x+2) and (g(x)=x-2+4x+4), what is (\left\(\frac{g}{f}\right\)(x))?
A. \(x+2,\ x\neq -2\)
(g(x)=(x+2)2), इसलिए (\frac{g(x)}{f(x)}=x+2), लेकिन \(x\neq -2\)। quotient में denominator की zero value हटानी जरूरी है। / (g(x)=(x+2)2), so (\frac{g(x)}{f(x)}=x+2), but \(x\neq -2\). In a quotient, remove the zero value of the denominator.
Login to save your score, XP, coins and progress.
If (f(x)=x-2-1) and (g(x)=x-2+1), what is ((fg)(x))?
A. \(x^4-1\)
(\(x^2-1\)\(x^2+1\)=x-4-1) difference of squares से मिलता है। formula पहचानने से calculation तेज होती है। / (\(x^2-1\)\(x^2+1\)=x-4-1) by difference of squares. Recognizing the formula makes calculation faster.
Login to save your score, XP, coins and progress.
If (f(x)=2x-7) and (g(x)=x+5), what is the value of ((f+g)(3))?
A. (7)
(f(3)=-1) और (g(3)=8), इसलिए ((f+g)(3)=7)। direct substitution सबसे सुरक्षित तरीका है। / (f(3)=-1) and (g(3)=8), so ((f+g)(3)=7). Direct substitution is the safest method.
Login to save your score, XP, coins and progress.
If (f(x)=x-2) and (g(x)=x+1), what is ((f-g)(0))?
A. (-1)
(f(0)=0) और (g(0)=1), इसलिए ((f-g)(0)=0-1=-1)। (0) पर value रखते समय constant term न भूलें। / (f(0)=0) and (g(0)=1), so ((f-g)(0)=0-1=-1). At (0), do not forget the constant term.
Login to save your score, XP, coins and progress.
If (f(x)=\frac{2}{x+3}) and (g(x)=\frac{1}{x-1}), what is the domain of ((f+g)(x))?
A. \(\mathbb{R}-{-3,1}\)
दोनों denominators non-zero होने चाहिए, इसलिए \(x\neq -3\) और \(x\neq 1\)। rational functions में सभी denominators check करें। / Both denominators must be non-zero, so \(x\neq -3\) and \(x\neq 1\). For rational functions, check all denominators.
Login to save your score, XP, coins and progress.
If (f(x)=x-4) and (g(x)=x-2+2x), what is ((g+f)(x))?
A. \(x^2+3x-4\)
((g+f)(x)=g(x)+f(x)=x-2+2x+x-4=x-2+3x-4)। addition में order बदलने से answer नहीं बदलता। / ((g+f)(x)=g(x)+f(x)=x-2+2x+x-4=x-2+3x-4). In addition, changing the order does not change the answer.
Login to save your score, XP, coins and progress.
If (f(x)=x-2+3) and (g(x)=2x), what is ((fg)(1))?
A. (8)
(f(1)=4) और (g(1)=2), इसलिए ((fg)(1)=4\cdot2=8)। product में values multiply होती हैं। / (f(1)=4) and (g(1)=2), so ((fg)(1)=4\cdot2=8). In a product, the function values are multiplied.
Login to save your score, XP, coins and progress.
If (f(x)=x-2-2x) and (g(x)=x-2), what is the simplified form of (\left\(\frac{f}{g}\right\)(x))?
A. \(x,\ x\neq 2\)
(\frac{x-2-2x}{x-2}=\frac{x(x-2)}{x-2}=x), पर \(x\neq 2\)। cancelled factor से मूल restriction खत्म नहीं होती। / (\frac{x-2-2x}{x-2}=\frac{x(x-2)}{x-2}=x), but \(x\neq 2\). A cancelled factor does not remove the original restriction.
Login to save your score, XP, coins and progress.
If (f(x)=\sqrt{x+2}) and (g(x)=\frac{1}{x-1}), what is the domain of ((f+g)(x))?
A. \([-2,\infty\)-{1})
\(\sqrt{x+2}\) के लिए \(x\geq -2\) और \(\frac{1}{x-1}\) के लिए \(x\neq 1\)। intersection से domain \([-2,\infty\)-{1}) मिलता है। / For \(\sqrt{x+2}\), \(x\geq -2\), and for \(\frac{1}{x-1}\), \(x\neq 1\). Their intersection gives \([-2,\infty\)-{1}).
Login to save your score, XP, coins and progress.
If (f(x)=x+1) and (g(x)=\frac{1}{x+1}), what is the value of ((fg)(x))?
A. \(1,\ x\neq -1\)
((fg)(x)=(x+1)\cdot\frac{1}{x+1}=1), पर (x=-1) allowed नहीं है। reciprocal वाली function में denominator check करें। / ((fg)(x)=(x+1)\cdot\frac{1}{x+1}=1), but (x=-1) is not allowed. Always check the denominator in a reciprocal function.
Login to save your score, XP, coins and progress.
If (f(x)=x-2+1) and (g(x)=x-2-1), what is ((f-g)(x))?
A. (2)
((f-g)(x)=x-2+1-\(x^2-1\)=2)। bracket हटाते समय (-1) का sign बदलकर (+1) होता है। / ((f-g)(x)=x-2+1-\(x^2-1\)=2). While removing the bracket, the sign of (-1) changes to (+1).
Login to save your score, XP, coins and progress.
If (f(x)=x+5) and (g(x)=2x-1), what is ((2f-3g)(x))?
A. (-4x+13)
((2f-3g)(x)=2(x+5)-3(2x-1)=-4x+13)। coefficients को पूरी function पर लागू करें। / ((2f-3g)(x)=2(x+5)-3(2x-1)=-4x+13). Apply coefficients to the whole function.
Login to save your score, XP, coins and progress.
Use Google login or mobile OTP. Admin can block users and control login providers.