Question

If f(x)=x^2+9x+5 and g(x)=5x-1, find (fg)(5)

Answer 1

This problem is a combination of functions, or doing a specific operation to two different function.

Here, we se the rule (fg)(5).

The product rule for functions can be written like this:

$(fg)(x)=f(x)\cdot g(x)$

We will multiply our two functions, f(x) and g(x) together. Since we have an x value of 5, we can think of it like this:

$f(5)\cdot g(5)$

First, let's find f(5).

$\begin{gathered} f(5)=(5)^2+9(5)+5 \\ f(5)=25+45+5 \\ f(5)=75 \end{gathered}$

Next, let's evaluate g(5).

$\begin{gathered} g(5)=5(5)-1 \\ g(5)=25-1 \\ g(5)=24 \end{gathered}$

Finally, we will multiply f(5) and g(5).

$\begin{gathered} f(5)\cdot g(5) \\ 75\cdot24 \\ 1800 \end{gathered}$

So, our final answer is 1800.