Question

If function F is defined by f(x) = 3x^2 + 5, what is f(x-4)

Answer 1

The function f(x) when x=x-4 is
`f(x-4)=3x^2-24x+53` or
`f(x-4)=3x(x-8)+53`

Explanation:

Given function f is defined by
`f(x)=3x^2+5`

Now to find the function f(x-4):

`f(x)=3x^2+5`

Put x=x-4 in the above function we get

`f(x-4)=3(x-4)^2+5`

`f(x-4)=3(x^2-2(x)(4)+4^2)+5` (using the formula
`(a-b)^2=a^2-2ab+b^2`)

`f(x-4)=3(x^2-8x+16)+5`

`f(x-4)=3x^2-24x+48+5` (adding the like terms)

`f(x-4)=3x^2-24x+53`

`f(x-4)=3x(x-8)+53`

Therefore
`f(x-4)=3x^2-24x+53` or
`f(x-4)=3x(x-8)+53`

The function f(x) when x=x-4 is
`f(x-4)=3x^2-24x+53` or
`f(x-4)=3x(x-8)+53`