PYQ Vault
EbooksTutor

Is a composite fog one-one or onto

This type of question, asked 3 times: 2021 Paper 1, 26 Jun 2022, 5 Apr 2024. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 1

    66
    Let f:R→Rf:R\rightarrow R be defined as f(x)=2x−1f(x) = 2x- 1 and g:R−{1}→Rg:R\mathbf{- \{ 1\} \rightarrow}R be defined as g(x)=x−12x−1g(x) =\frac{x-\frac{1}{2}}{x- 1}. Then the composition function f(g(x))f(g(x)) is:

    Tap an option to check your answer.

  2. Question 2

    26 Jun 2022

    151
    Let f:R→Rf:R \rightarrow R be defined as f(x)=x−1f(x) = x - 1 and g:R−{1,−1}→R\mathbf{g:R - \{ 1, - 1\} \rightarrow R} be defined as g(x)=x2x2−1g(x) =\frac{x^{2}}{x^{2}- 1}. Then the function fog is:

    Tap an option to check your answer.

  3. Question 3

    5 Apr 2024

    161
    Let f, g:R→Rf,\text{ }g:R \rightarrow R be defined as: f(x)=∣x−1∣f(x) = |x - 1| and g(x)={ex,x≥0x+1,x≤0g(x) =\left\{ \begin{matrix} e^{x}, & x \geq 0 \\ x + 1, & x \leq 0 \end{matrix} \right.. Then the function f( g(x))f(\text{ }g(x)) is

    Tap an option to check your answer.