Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
Difficulty select karke sirf is topic ke focused MCQs practice karein. Score, timer aur explanations student-friendly flow me milenge.
Showing 151-160 of 600 questions.
If (f(x)=2x+3) and (g(x)=x-2-1), what is ((f+g)(x))?
A. \(x^2+2x+2\)
((f+g)(x)=f(x)+g(x)), इसलिए \(2x+3+x^2-1=x^2+2x+2\)। परीक्षा में like terms को साथ जोड़ें। / ((f+g)(x)=f(x)+g(x)), so \(2x+3+x^2-1=x^2+2x+2\). In exams, combine like terms carefully.
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If (f(x)=x-2+4x) and (g(x)=3x-5), find ((f-g)(x)).
A. \(x^2+x+5\)
((f-g)(x)=f(x)-g(x)), अतः (x-2+4x-(3x-5)=x-2+x+5)। घटाते समय bracket का sign बदलता है। / ((f-g)(x)=f(x)-g(x)), hence (x-2+4x-(3x-5)=x-2+x+5). While subtracting, change the signs inside the bracket.
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If (f(x)=x+2) and (g(x)=x-3), what is ((fg)(x))?
A. \(x^2-x-6\)
((fg)(x)=f(x)g(x)), इसलिए ((x+2)(x-3)=x-2-x-6)। गुणा में दोनों terms को distribute करें। / ((fg)(x)=f(x)g(x)), so ((x+2)(x-3)=x-2-x-6). In multiplication, distribute both terms properly.
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If (f(x)=x-2-9) and (g(x)=x-3), what is the simplified form of (\left\(\frac{f}{g}\right\)(x))?
A. \(x+3,\ x \neq 3\)
(\frac{x-2-9}{x-3}=\frac{(x-3)(x+3)}{x-3}=x+3), पर (x=3) allowed नहीं है। cancel करने के बाद भी मूल denominator याद रखें। / (\frac{x-2-9}{x-3}=\frac{(x-3)(x+3)}{x-3}=x+3), but (x=3) is not allowed. Even after cancellation, remember the original denominator.
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If (f(x)=\sqrt{x-1}) and (g(x)=\sqrt{5-x}), what is the domain of ((f+g)(x))?
A. ([1,5])
दोनों square roots defined होने चाहिए, इसलिए \(x-1\geq 0\) और \(5-x\geq 0\), जिससे \(x\in[1,5]\)। sum के लिए domains का intersection लें। / Both square roots must be defined, so \(x-1\geq 0\) and \(5-x\geq 0\), giving \(x\in[1,5]\). For a sum, take the intersection of domains.
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If (f(x)=\frac{1}{x-2}) and (g(x)=x+4), what is the domain of ((f+g)(x))?
A. \(\mathbb{R}-{2}\)
(f(x)) में denominator (x-2) शून्य नहीं हो सकता, इसलिए \(x\neq 2\)। polynomial (g(x)) सभी real (x) पर defined है। / In (f(x)), the denominator (x-2) cannot be zero, so \(x\neq 2\). The polynomial (g(x)) is defined for all real (x).
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If (f(x)=x-2) and (g(x)=2x+1), what is the value of ((f+g)(-1))?
A. (0)
((f+g)(-1)=f(-1)+g(-1)=1+(-1)=0)। पहले functions में value रखें, फिर जोड़ें। / ((f+g)(-1)=f(-1)+g(-1)=1+(-1)=0). First substitute the value in each function, then add.
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If (f(x)=3x-2) and (g(x)=x-2+1), what is ((g-f)(2))?
A. (1)
(g(2)=5) और (f(2)=4), इसलिए ((g-f)(2)=5-4=1)। order को ध्यान से पढ़ें क्योंकि (g-f) और (f-g) अलग होते हैं। / (g(2)=5) and (f(2)=4), so ((g-f)(2)=5-4=1). Read the order carefully because (g-f) and (f-g) are different.
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If (f(x)=x+1), (g(x)=x-1), and (h(x)=x-2), what is ((f+g+h)(x))?
A. \(x^2+2x\)
((f+g+h)(x)=(x+1)+(x-1)+x-2=x-2+2x)। constants (1) और (-1) cancel हो जाते हैं। / ((f+g+h)(x)=(x+1)+(x-1)+x-2=x-2+2x). The constants (1) and (-1) cancel out.
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If (f(x)=2x-2-1), what is ((3f)(x))?
A. \(6x^2-3\)
((3f)(x)=3f(x)=3\(2x^2-1\)=6x-2-3)। scalar को पूरी function से multiply करें। / ((3f)(x)=3f(x)=3\(2x^2-1\)=6x-2-3). Multiply the scalar by the whole function.
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