Answer:
see explanation
Step-by-step explanation:
(i)
to find h(g(x)) , substitute x = g(x) into h(x) , that is
h(g(x))
= h(2x - 3)
= 4(2x - 3)
= 8x - 12
(ii)
given
h(g(x)) = [tex]\frac{1}{2}[/tex] g(x) , then
8x - 12 = [tex]\frac{1}{2}[/tex] (2x - 3) ← multiply both sides by 2 to clear the fraction
16x - 24 = 2x - 3 ( subtract 2x from both sides )
14x - 24 = - 3 ( add 24 to both sides )
14x = 21 ( divide both sides by 14 )
x = [tex]\frac{21}{14}[/tex] = [tex]\frac{3}{2}[/tex] = 1.5
