How can we solve for fg(x) given f(x)=2x+5 and g(x)=x-7 when x = -3?

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To solve for fg(x), we first need to properly define what this expression means. The notation fg(x) means we will find g(x) first and then use that result as the input for f(x).

Given the functions:

  • f(x) = 2x + 5
  • g(x) = x – 7

We will begin by substituting x = -3 into g(x):

g(-3) = -3 - 7 = -10

Next, the output of g(-3), which is -10, will be used as the input for f(x):

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

Now we will calculate f(-10):

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

So, the composition fg(x) when x = -3 is:

fg(-3) = f(g(-3)) = -15

Therefore, the final result is:

fg(-3) = -15

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