CAT 2025 Functions Question (Hard)

Question

Let and . Then, the domain of the function is all real numbers except

Accepted Answer

We check where f x 2x-1 or g x x-1 , or their compositions, become undefined. First, f x is undefined at x tfrac12 and g x is undefined at x 1. Next, for f g x x 1 Since, the denominator can t be zero, x -1 must also be excluded. For g f x 1-x Rightarrow x 1 is not possible, which is already exclude

CAT 2025

Quantitative

Functions

Hard

Let $f(x) = \dfrac{x}{(2x-1)}$ and $g(x) = \dfrac{x}{(x-1)}$ . Then, the domain of the function $h(x) = f(g(x)) + g(f(x))$ is all real numbers except

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