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

Expert Answers

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(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` .

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