Question

If f(x) = 2x + 3 and g(x) = x2 + 1,find f(g(3)). 23 47 82 90

Answer 1

Hi!

So, this is going to be a function composition problem.

How we solve this, is by solving the function g(x). The output value we receive from solving g(x), is then the value that we input into the function f(x). 

So if g(x) equals something like 2, then we will input 2 into the function f(x).

Let's go ahead and solve g(3).

g(3) = 3^2 + 1.

First, we must solve the exponent due to the order of operations.

g(3) = 9 + 1.

Now we simply add 9 and 1.

g(3) = 10.

Okay, so - g(3) is equal to 10. Now we will input this value into f(x)!

f(10) = 2(10) + 3.

Again, we must follow the order of operations - so we will multiply 2 and 10 first.

f(10) = 20 + 3.

Now we add 20 and 3.

f(10) = 23.

Our final answer for this composite function is 23!

Hopefully, this helps! =)