3.15: Logarithmic domain and composite with a quadratic

0606/22/O/N/25 — Question 9 · 5 marks

It is given that

f(x) = \ln(2x + 5)

for

x > a

, where

a

is a constant.

(a)

Write down the least possible value of

a

[1]

(b)

Using your value of

a

, write down the range of

f

[1]

(c)

It is also given that

g(x) = x^{2} + 1

for

x \in \mathbb{R}

Using your value of

a

, solve the equation

fg(x) = 4

. Give your answers in exact form.

[3]