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 201-210 of 600 questions.
If (f(x)=x-2+1) and (g(x)=2x-3), what is ((f+g)(x))?
A. \(x^2+2x-2\)
((f+g)(x)=f(x)+g(x)=x-2+1+2x-3=x-2+2x-2)। परीक्षा में समान पदों को ध्यान से जोड़ें। / ((f+g)(x)=f(x)+g(x)=x-2+1+2x-3=x-2+2x-2). In exams, combine like terms carefully.
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If (f(x)=3x+5) and (g(x)=x-2-4), find ((g-f)(x)).
A. \(x^2-3x-9\)
((g-f)(x)=g(x)-f(x)=x-2-4-(3x+5)=x-2-3x-9)। घटाते समय पूरे (f(x)) पर ऋण लगाएँ। / ((g-f)(x)=g(x)-f(x)=x-2-4-(3x+5)=x-2-3x-9). While subtracting, apply the minus sign to the whole (f(x)).
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If (f(x)=x+2) and (g(x)=x-5), what is ((fg)(x))?
A. \(x^2-3x-10\)
((fg)(x)=f(x)g(x)=(x+2)(x-5)=x-2-3x-10)। गुणा में विस्तार के बाद समान पद मिलाएँ। / ((fg)(x)=f(x)g(x)=(x+2)(x-5)=x-2-3x-10). After expanding, combine like terms.
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If (f(x)=x-2-9) and (g(x)=x-3), what is (\left\(\frac{f}{g}\right\)(x)) for \(x \neq 3\)?
A. (x+3)
(\left\(\frac{f}{g}\right\)(x)=\frac{x-2-9}{x-3}=\frac{(x-3)(x+3)}{x-3}=x+3), जहाँ \(x \neq 3\)। हर शून्य न हो, यह हमेशा जाँचें। / (\left\(\frac{f}{g}\right\)(x)=\frac{x-2-9}{x-3}=\frac{(x-3)(x+3)}{x-3}=x+3), where \(x \neq 3\). Always check that the denominator is not zero.
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If (f(x)=\frac{1}{x-2}) and (g(x)=\frac{1}{x+4}), what is the domain of ((f+g)(x))?
A. \(x \in \mathbb{R}, x \neq 2, x \neq -4\)
हरों (x-2) और (x+4) को शून्य नहीं होना चाहिए, इसलिए \(x \neq 2\) और \(x \neq -4\)। परिमेय फलनों में हर पहले जाँचें। / The denominators (x-2) and (x+4) must not be zero, so \(x \neq 2\) and \(x \neq -4\). In rational functions, check denominators first.
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If (f(x)=2x-2) and (g(x)=x+1), what is the value of ((f-g)(-2))?
A. (9)
((f-g)(x)=2x-2-(x+1)), इसलिए ((f-g)(-2)=8-(-1)=9)। पहले फलन बनाकर फिर मान रखें। / ((f-g)(x)=2x-2-(x+1)), so ((f-g)(-2)=8-(-1)=9). First form the function, then substitute the value.
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If (f(x)=x-2+2x) and (g(x)=x-2-2x), what is ((f+g)(3))?
A. (18)
((f+g)(x)=2x-2), अतः ((f+g)(3)=2\cdot 32=18)। विरोधी पद कट सकते हैं, इसलिए सरल रूप देखें। / ((f+g)(x)=2x-2), hence ((f+g)(3)=2\cdot 32=18). Opposite terms may cancel, so simplify first.
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If (f(x)=x-2-1) and (g(x)=2x+1), find ((fg)(2)).
A. (15)
((fg)(2)=f(2)g(2)=(4-1)(5)=15)। उत्पाद में दोनों फलनों का मान अलग-अलग निकालना आसान है। / ((fg)(2)=f(2)g(2)=(4-1)(5)=15). In a product, finding both values separately is often easier.
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If (f(x)=4x-1) and (g(x)=x-2+2), which statement about ((g+f)(x)) and ((f+g)(x)) is correct?
A. दोनों बराबर हैंBoth are equal
फलनों का योग क्रमविनिमेय है, इसलिए ((f+g)(x)=(g+f)(x))। योग में क्रम बदलने से मान नहीं बदलता। / Addition of functions is commutative, so ((f+g)(x)=(g+f)(x)). Changing order in addition does not change the value.
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If (f(x)=x+6) and (g(x)=x-6), what is the simplified form of ((fg)(x))?
A. \(x^2-36\)
((fg)(x)=(x+6)(x-6)=x-2-36)। यह \(a^2-b^2\) का पैटर्न है। / ((fg)(x)=(x+6)(x-6)=x-2-36). This follows the \(a^2-b^2\) pattern.
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