Question

If f(x)=x+2 and g(x)=x2+1 find:a. f(g(x)) b. g(f(x))

Answer 1

x² + 3 and x² + 4x + 5

Explanation:

(a)

to find f(g(x)) substitute x = g(x) into f(x)

f(g(x))

= f(x² + 1)

= x² + 1 + 2

= x² + 3

(b)

to find g(f(x)) substitute x = f(x) into g(x)

g(f(x))

= g(x + 2)

= (x + 2)² + 1 ← expand factor using FOIL

= x² + 4x + 4 + 1

= x² + 4x + 5

Answer 2

Explanation: