How do you solve for fg(x) when given f(x) = 2x + 5 and g(x) = x – 7, specifically for x = -3?

To find fg(x), we need to first determine g(x) and then use that result to find f(g(x)).

Given the functions:

• f(x) = 2x + 5
• g(x) = x – 7

Let’s start by calculating g(-3):

g(-3) = -3 – 7 = -10

Now that we have g(-3), we can plug this result into f(x):

f(g(-3)) = f(-10)

Now, let’s calculate f(-10):

f(-10) = 2(-10) + 5 = -20 + 5 = -15

So, fg(-3) = f(g(-3)) = f(-10) = -15.

In conclusion, the value of fg(-3) is -15.