Question

Given that f(x) = x2 + 5x – 14 and g(x) = x + 7, find (fºg)(x) and express

the result in standard form.

Answer 1

We get
`\mathbf{(fog)(x)=x^3+12x^2+21x-98}`

Explanation:

We are given:

`f(x) = x^2 + 5x - 14 \\ g(x) = x + 7`

We need to find
`(f o g)(x)`

We know that:
`(fog)(x)=f(x)* g(x)`

We multiply the both terms i.e. f(x) and g(x) to get our answer.

`(fog)(x)\\=f(x)* g(x)\\=(x^2+5x-14)(x+7)\\=(x^2+5x-14)(x)+(x^2+5x-14)(7)\\=x^3+5x^2-14x+7x^2+35x-98\\Combining\:like\:terms:\\=x^3+5x^2+7x^2-14x+35x-105\\=x^3+12x^2+21x-98`

So, we get
`\mathbf{(fog)(x)=x^3+12x^2+21x-98}`