# 1.6 Function, SPM Practice (Long Question)

Question 1:
The function f and g is defined by
$\begin{array}{l}f:x↦2x-3\\ g:x↦\frac{2}{x};x\ne 0\end{array}$
Find the expression for each of the following functions
(a) ff,
(b) gf,
(c) f-1 ,
Calculate the value of x such that ff(x) = gf(x).

Solution:
(a)

(b)

(c)

Question 2:
The function f and g is defined by

Solution:
(a)

(b)

(c)

(d)
$\begin{array}{l}f\left[k\left(x\right)\right]=4x-7\\ 3k\left(x\right)-2=4x-7\\ 3k\left(x\right)=4x-5\\ k\left(x\right)=\frac{4x-5}{3}\end{array}$