Let and define three bijective functions: , ; , ; ,

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

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}

(b)

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

(c)

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

(d)

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

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