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Question

Let f(x)=3x+9 and g(x)=x^2 - 5

Find the following.

(g o f)(-5)

Answer 1

Function composition isn't terribly complicated, at least not in questions like this one, but it is also critical to future math courses like trig and calculus. 

Basically, (gºf)[x] means g [ fX) ]. In your case, that means:

(gºf)[-5] = g [ f(-5) ]

Since f(X) = 3X+9, f(-5) = 3(-5) + 9 = -15 + 9 = -6

Now, we have: 

g (-6)

Since we know g(X) = x² - 5 , that means

g(-6) = (-6)² - 5 = 36 - 5 = 31

Ta-da! The answer is 31!