Question

For f(x)=2-x and g(x)=4x^2+x+6, find (f×g)(x)

Answer 1

Our composed function is
`f(g(x)) = -4x^2-x-4`.

Explanation:

We are given two separate functions:

`f(x) = 2-x`

`g(x) = 4x^2 + x + 6`

We need to find the composition of
`(f \cdot g)(x)`. This is literally stating "f of g of x."

Therefore, we simply plug g(x) into f(x) and solve. We replace the x-value in the f(x) function with the entirety of the g(x) function and simplify.

`f(g(x)) = 2 - (4x^2+x+6)\\\\f(g(x)) = 2 - 4x^2 + x + 6\\\\f(g(x)) = -4x^2 - x - 4`

Our composed function is
`f(g(x)) = -4x^2-x-4`.