JEE PYQ: Functions Question 6
Question 6 - 2021 (24 Feb Shift 1)
Let $\mathbf{f} : \mathbb{R} \to \mathbb{R}$ be defined as $\mathbf{f}(\mathbf{x}) = 2x - 1$ and $g : \mathbb{R} - {1} \to \mathbb{R}$ be defined as $g(x) = \frac{x - \frac{1}{2}}{x - 1}$. Then the composition function $f(g(x))$ is:
(1) both one-one and onto
(2) onto but not one-one
(3) neither one-one nor onto
(4) one-one but not onto
Type: MCQ
Show Answer
Answer: (4) one-one but not onto
Solution
$f(g(x)) = \frac{x}{x-1} = 1 + \frac{1}{x-1}$
one-one, into (not onto)
BETA
