Question

If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (g – f)(3)?

A.6 – 3 – (4 + 3)^2
B,6 – 3 – (4 – 3^2)
C.6(3) – 4 + 3^2
D.6(3) – 4 – 3^2

Answer 1

Remember that
`(g-f)(x)` is
`g(x)-f(x)`. We know form our problem that
`f(x)=4-x^2` and
`g(x)=6x`, so:

`(g-f)(x)=g(x)-f(x)`

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

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

Now, to find
`(g-f)(3)`, we just need to evaluate
`(g-f)(x)` at 3. In other words, we are going to replace
`x` with 3:

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

`(g-f)(x)=6(3)-4+(3)^2`

We can conclude that the correct answer is C.6(3) – 4 + 3^2