Composite Functions

x*h(x)=4*x^2-5*x
f(x)+x*h(x)=4*x^2-5*x+3*x+1=4*x^2-2*x+1
g(x)=3*x+1
g(f(x)+x*h(x))=g(4*x^2-2*x+1)
(4*x^2-2*x+1)=x
g(4*x^2-2*x+1)=3*(4*x^2-2*x+1)+1=12*x^2+4-6*x

f(x) = x^3 – 1 • g(x)=3x+1 • h(x) = 4x – 5. Show that g(f(x)) + xh(x) = 3x^3 + 4x2 – 5x – 2.

g(f(x)  =  3(x^3 -1) + 1  =  3x^3 - 3  + 1  =  3x^3 - 2

x* h(x)  = x* (4x - 5)   =  4x^2 - 5x

So.......combining both results - as was specified-  we get :

3x^3 + 4x^2 - 5x  - 2