Part A
Given: f(x) = x - 7
(a)
y = x - 7 [make x the subject]
x = y + 7 [this is the inverse]
f⁻¹(x) = x + 7
(b)
(f × f⁻¹)(x) = x [go right to left in such function]
f(x + 7) = x
(x - 7) + 7 = x
x = x
Part B
Given: g(x) = 12x
(a)
y = 12x [make x the subject]
x = y/12 [this is the inverse]
g⁻¹(x) = x/12
(b)
(g × g⁻¹)(x) = x [go right to left in such function]
g(x/12) = x
12x/12 = x [simplify]
x = x