Mathematics - Functions Question with Solution | TestHub

$f\left(g\left(x\right)\right)=2g\left(x\right)-1=2\left(\frac{2x-1}{2\left(x-1\right)}\right)-1.$

$=\frac{x}{x-1}=1+\frac{1}{x-1}$

Range of $f\left(g\left(x\right)\right)=R-\left\{1\right\}$

Range of $f\left(g\left(x\right)\right)$ is not onto

& $f\left(g\left(x\right)\right)$ is one-one

So $f\left(g\left(x\right)\right)$ is one-one but not onto.

one-one, into