Question

F(x)=x+3
g(x) = 2x² - 4
Find (f. g)(x).

Answer 1

`(f \cdot g)(x)` =
`2x^2 -1`

Explanation:

`(f \cdot g)(x)`, read as "f of g of x", means we have to use the function
`\bf g(x)` as input for the function
`\bf f(x)`. This means, we have to replace the
`x` in the definition of
`f(x)` with
`g(x)`.

`f(x)=x+3`

`g(x) = 2x^2 - 4`

∴
`(f \cdot g)(x) = f(g(x))`

⇒
`g(x) + 3`

⇒
`(2x^2 - 4) + 3`

⇒
`2x^2 -1`