Mathematics

Problem

Let

k\neq 0

and define three bijective functions:

f:\mathbb R\to\mathbb R

f(x)=kx+1

;

g:\mathbb R\setminus\{0\}\to\mathbb R\setminus\{0\}

g(x)=\dfrac{1}{x}

;

h:\mathbb R\to\mathbb R

h(x)=x^{5}

. If

F=h\circ g\circ f

, then

F^{-1}(x)

equals a)

\dfrac{x^{1/5}-1}{k}

k\,x^{-1/5}-1

\dfrac{x^{-1/5}-1}{k}

\dfrac{1-x^{1/5}}{k}