JEE Main 2021 · 24 Feb · Shift 1 · Mathematics Q61

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MathematicsSingle correct+4 / -1Question 61 of 90

Let $f:\mathbf R\to\mathbf R$ be defined as $f(x)=2x-1$ and $g:\mathbf R-\{1\}\to\mathbf R$ be defined as $g(x)=\dfrac{x-\frac12}{x-1}$ . Then the composition function f(g(x)) is :

one-one but not onto

onto but not one-one

neither one-one nor onto

both one-one and onto

Answer and worked solution

Official answer: A

Compose. $f(g(x))=\dfrac{2x-1}{x-1}-1=\dfrac x{x-1}$ , which is one-one on $\mathbf R-\{1\}$ but never takes the value 1: not onto.

(A)

Topics:Composition and inverse functions Types of functions

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JEE Main 2021 · 24 Feb · Shift 1, Mathematics question 61