Let and , where is a real…

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

Problem

Let

f(x)=e^{x}

and

g(x)=\ln(kx+5)

, where

k

is a real parameter. (i) Obtain

(g\circ f)(x)

in its simplest form. (ii) Determine the set of all real values of

k

for which

(g\circ f)(x)

is defined for every

x\ge 0

. (iii) Using

k=2

, evaluate

(g\circ f)(\ln 3)

. Express your answer in exact form.