Let $D = \mathbb{R} - \{0, 1\}$ and $f: D \rightarrow D$,$g: D \rightarrow D$,and $h: D \rightarrow D$ be three functions defined by $f(x) = \frac{1}{x}$,$g(x) = 1 - x$,and $h(x) = \frac{1}{1 - x}$. If $j: D \rightarrow D$ is such that $(g \circ j \circ f)(x) = f(x)$ for all $x \in D$,then which one of the following is $j(x)$?

  • A
    $(f \circ g)(x)$
  • B
    $f(x)$
  • C
    $g(x)$
  • D
    $(g \circ h)(x)$

Explore More

Similar Questions

If $f(x) = x^2 + 1$,then $fof(x)$ is equal to

$f: R \rightarrow R$ and $g:[0, \infty) \rightarrow R$ are defined by $f(x)=x^2$ and $g(x)=\sqrt{x}$. Which one of the following is not true?

Let $f(x) = 1 - x$, $g(x) = \frac{1}{1 - x}$, and $h(x) = \frac{1}{x}$ be three functions, for $x \neq 0, 1$. If a function $F(x)$ satisfies $f(F(h(x))) = g(x)$, then which of the following is true?

If $f(x)=3x-2$ and $g(x)=x^2$,then $f \circ g(x) = \_\_\_\_$

If $g(x)=x^{2}+x-1$ and $(g \circ f)(x)=4 x^{2}-10 x+5,$ then $f\left(\frac{5}{4}\right)$ is equal to

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo