Question

If f(x) = x+4 and g(x) = 2x2-x-1, find the composition (f o g)(x).

Answer 1

(f º g)(x) = 2x² - x + 3

Explanation:

`(f\circ g)(x)=f\bigg(g(x)\bigg)\\\\f(x)=x+4,\ g(x)=x^2-x-1\\\\\text{Put}\ x=g(x)\ \text{in}\ f(x):\\\\(f\circ g)(x)=f\bigg(2x^2-x-1\bigg)=(2x^2-x-1)+4\\\\=2x^2-x-1+4\qquad\text{combine like terms}\\\\(f\circ g)(x)=2x^2-x+3`

Answer 2

2x² - x + 3

Explanation:

To find (f ￮ g)(x), substitute x = g(x) into f(x)

f(g(x)) = f(2x² - x - 1) = 2x² - x - 1 + 4 = 2x² - x + 3