Question

If s(x) = x – 7 and t(x) = 4x2 – x + 3, which expression is equivalent to (t*s)(x)

Answer 1

(t o s)(x) = t(s(x))
s(x) = x - 7
t(x - 7) = 4(x-7)^2 - (x - 7) + 3

Answer 2

`4(x-7)^2-(x-7)+3`

Explanation:

Given the functions:

`s(x)=x-7` and
`t(x)=4x^2-x+3`

We have to find the
`(t \circ s)(x)`

`(t \circ s)(x) = t(s(x))`

Substitute the function s(x) we have;

⇒
`t(s(x)) = t(x-7)`

Replace x with x-7 in t(x) we have;

⇒
`t(x-7) = 4(x-7)^2-(x-7)+3`

⇒
`(t \circ s)(x) = 4(x-7)^2-(x-7)+3`

Therefore, the expression which is equivalent to
`(t \circ s)(x)` is:

`4(x-7)^2-(x-7)+3`