Question

Let A,B,C ⊆ N and a function f: A → B be defined by f(x) = 2x + 1 and g: B → C be defined by g(x) = x². Find the range of fog and gof.

Answer 1

f(x) = 2x + 1; g(x) = x² 

fog = f[g(x)] 

= f(x²) 

= 2x² + 1 

2x² + 1 ∈ N 

gof = g [f(x)]

= g (2x + 1) 

gof = (2x + 1)² 

(2x + 1)² ∈ N 

Range = {y/y = 2x² + 1, x ∈ N}; 

{y/y = (2x + 1)², x ∈ N)