Let f, g :R → R be defined by f(x) = 2x + 1 and g (x) = x2 – 2, i∀ x ∈ R, respectively. Then, find g o f.
We have,
gof(x) = g(f(x))
⇒ gof(x) = g(2x+1)
= (2x+1)2 – 2
= (4x2+1+4x) – 2
= 4x2+4x-1
∴ gof = 4x2+4x-1