Question

If f(x) = (x − 3)2 + 4 and g(x) = x3 + 2, find g(–3) − f(–5).

Answer 1

Evaluating a function

In order to find:

g(–3) − f(–5),

we first want to find g(–3) and f(–5).

In order to find them we just have to replace x on their equations:

g(-3)

We just replace x by -3 in the equation

`\begin{gathered} g(x)=x^3+2 \\ \downarrow \\ g(-3)=(-3)^3+2 \end{gathered}`

And now, we solve it

`\begin{gathered} g(-3)=(-3)^3+2 \\ g(-3)=-27+2=-25 \end{gathered}`

Then, g(-3) = -25

f(-5)

We just replace x by -5 in the equation

`\begin{gathered} f(x)=(x-3)^2+4 \\ \downarrow \\ f(-5)=(-5-3)^2+4 \end{gathered}`

And now, we solve it

`\begin{gathered} f(-5)=(-5-3)^2+4 \\ f(-5)=(-8)^2+4=64+4 \\ =68 \end{gathered}`

then, f(-5) = 68

g(–3) − f(–5)

Since

g(-3) = -25

and

f(-5) = 68

then

g(–3) − f(–5) = -25 - 68 = -93

Answer: g(–3) − f(–5) = -93