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