Define for all

MATHEMATICS · Single correct · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Define

k(x)=x+1

for all

x\in\mathbb R

,

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

for

x\ne 0

, and

f(x)=x^{2}

for

x>0

. Let

h=f\circ g\circ k

. The inverse function

h^{-1}(x)

is (a)

-\dfrac{1}{\sqrt{x}}+1

(b)

\sqrt{x}-1

(c)

\dfrac{1}{\sqrt{x}}-1

(d)

\dfrac{1}{x^{2}}-1

Related theory

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