Question

Given ƒ(x) = x² + 4 and g(x) = 5x − 3, find (ƒ ○ ƒ)(x).

Answer 1

The functions f (x ) = x ² + 4 and g (x ) = 5x - 3

(f of )(x ) = f (f (x ))

Substitute the expression for functioning f  (in this case x ² + 4 ) for f (x ) in the composition.

= f (x ² + 4)

Now substitute this expression (x ² + 4) in to function f  in place of the x  value.

= (x ² + 4)² + 4

(a + b )² = a ² + b ² + 2ab

a = x ²  and b = 4

= x ⁴ + 16 + 8x ² + 4

= x ⁴ + 8x ² + 20

(f of )(x ) = x ⁴ + 8x ² + 20.