Question

Let $D=R-\\{0,1\\}$ 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 $(gojof)$ $(x)=f(x)$ for all $x \in D$, then which one of the following is $j(x) ?$

• A. $( fog )(x)$
• B. $f(x)$
• C. $g(x)$
• D. $(goh) (x)$

Answer 1

Answer: (C)

$g(x)$

Answer 2

We have,