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JEE MATHEMATICS MCQ: FUNCTIONS

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Assertion: If f(x)=1x−2,x≠2f(x)=\frac{1}{x-2}, x \neq 2 and g(x)=(x−2)2g(x)=(x-2)^2, then (f+g)(x)=1+(x−2)3x−2,x≠2({f}+{g})({x})=\frac{1+({x}-2)^3}{{x}-2}, {x} \neq 2.

Reason : If ff and gg are two functions, then their sum is defined by (f+g)(x)=f(x)+g(x) ∀ x∈D1∩D2({f}+{g})({x})={f}({x})+{g}({x}) \, \forall \, {x} \in {D}_1 \cap {D}_2, where D1D_1 and D2D_2 are domains of ff and gg, respectively.
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Correct option: A
Assertion is correct, Reason is correct; Reason is a correct explanation for assertion
Assertion is correct, Reason is correct; Reason is a correct explanation for assertion because the sum of two functions is defined as the sum of their individual values at each point in the intersection of their domains.

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