Mathematics

Problem

Let

h: \mathbb{R} \to \mathbb{R}

be defined by

h(x) = 5e^{2x} - 7

. a. (i) Prove that

h

is one–one and onto. b. (ii) Obtain

h^{-1}(x)

. c. (iii) Using your result, solve

h^{-1}(13) = k

and find the value of

k