Let be defined by

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Let

h:[0,8]\to\mathbb R

be defined by

h(t)=\sqrt{5t+1}

. Respond to the tasks below. (i) Determine the range of

h

. (ii) Find the explicit form of

h^{-1}(x)

. (iii) State the domain and the range of

h^{-1}

, giving each in interval notation. (iv) Prove that both

h

and

h^{-1}

are strictly increasing on their respective domains.