Find (f of g)(3) and (g of f)(-2)

Question

1). f(x)=2x-3; g(x)=x+1

2). f(x)=x/x+1; g(x)=9-x^2

Answer 1

When you have compositions of functions like these, you want to work from the inside out.

a) It helps re re-write (f of g)(3) as f( g(3) ) then work on the inside first { the g(3) part }

g(3)= 3 +1 = 4

Then you will substitute 4 into where g(3) was in your original problem.

f( g(3) )= f( 4 ) = 2(4)-3=5

So (f of g)(3)=5

*You can also think of it as plugging 3 into the function closest to it first then plug that answer into the farther function. Since g was closer, we plugged 3 into g(x) and took its answer and plugged it into f(x)

b) (g of f)(-2) can be re-written as g( f(-2) )then work from the inside out.

f(-2)= -2/(-2+1) = -2/-1 = 2

Then plug that answer into g(x)

g( f(-2) )= g( 2 ) = 9-(2)^2 = 9-4 = 5

Hope this helps!