# Evaluate the composite funcitons: Using f(x)= x-2 and g(x)= 5x+3 Find: a) f(g(2)) b) (g o f)(-4)

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Expert Answers

lemjay | Certified Educator

(A) `f(g(2))=?`

To solve, start with the function f(x).

`f(x)=x-2`

Then, replace the x with g(x).

`f(g(x))=g(x)-2`

After that, substitute g(x)=5x+3.

`f(g(x))= 5x+3-2`

`f(g(x))=5x+1`

And, plug-in x=2.

`f(g(2))=5(2)+1`

`f(g(2))=11`

**Therefore, `f(g(2))=11` .**

B.` (gof)(-4)=?`

Take note that (gof)(-4) is the same as g(f(-4)).So to solve, start with the function g(x).

`g(x)=5x+3`

Then, replace the x with f(x).

`g(f(x))=5f(x) + 3`

Then, substitute f(x) =x-2.

`g(f(x))=5(x-2) +3`

`g(f(x))=5x-10+3`

`g(f(x))=5x-7`

And, plug-in x=-4.

`g(f(-4))=5(-4)-7`

`g(f(-4))=-20-7`

`g(f(-4))=-27`

**Therefore `(gof)(-4)=-27` .**