Find the formula and domain of H

Question

Suppose that 

f(x)= 5x²+8x and 

g(x)=5x-5

 

For each function h given below, find a formula for h(x) and the domain of h in interval notation

A) h(x)= (fοg)(x)

   h(x)=

   domain=

B) h(x)=(gοf)(x)

    h(x)=

    domain=

C) h(x)=(fοf)(x)

    h(x)=

    domain=

D) h(x)=(gοg)(x)

     h(x)=

     domain=

 

 

 

Answer 1

A) h(x)= (f?g)(x) h(x)= f(g(x))=f(5x-5)=5(5x-5)^2 +8(5x-5) domain= (-infinite, + infinite) B) h(x)=(g?f)(x) h(x)=g(f(x))=g(5x^2 +8x)=5(5x^2 +8x) - 5 domain=(-infinite, + infinite) C) h(x)=(f?f)(x) h(x)= f(f(x))= f(5x^2+8x)=5(5x^2+8x)^2 +8(5x^2+8x) domain=(-infinite, + infinite) D) h(x)=(g?g)(x) h(x)= g(g(x))=g(5x-5)=5(5x-5) -5 domain=(-infinite, + infinite), each value of x that defines the above function h(x)