Determine the composition function(Proofs)

[shivers20]

R ---> R defined by f(x)= 2x+3 is one-to-one and onto.
R ---> R defined by g(x)= -3x+5 is one-to-one and onto.

I have completed the proofs for both but it is now asking me to determine the composition function g o f

I have (g o f) (x)= g(f(x))= g(2x+3)= -3(2x+3)+5= -6x-9+5= -6x-4
Is this correct, end of the proof? I learned this back in Calculus 1. Do I need more? Thanks in advance.

 

[daon]

If it said to find the composition then your answer makes sense to me. Odd that you'd be asked such an easy question. Maybe your teacher wanted you to realize that the composition is also a bijection (which it always will be if g and f are bijections). No idea really, though.