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.

Question

Let f, g :R → R be defined by f(x) = 2x + 1 and g (x) = x 2 – 2, i ∀ x ∈ R, respectively. Then, find g o f.

Philoid · Accepted Answer

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

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.