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

Let $S, T, U$ be three non-void sets and $f: S \rightarrow T, g: T \rightarrow U$ be functions such that $g \circ f: S \rightarrow U$ is surjective. Then,

If $f: R \rightarrow R$ is defined by $f(x) = \frac{x}{x^{2}+1}$,find $f(f(2))$.

If $f$ and $g$ are two increasing functions such that $fog$ is defined,then what kind of function is $fog$?

If $f(x) = (p - x^n)^{1/n}$,$p > 0$ and $n$ is a positive integer,then $f[f(x)]$ is equal to

If $R$ is a relation from a set $A$ to a set $B$ and $S$ is a relation from $B$ to a set $C$,then the relation $S \circ R$ is:

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