If u(x)=4x-5, v(x)=x^2, and f(x)=1/x, find formulas for,
u(v(f(x)))=
u(f(v(x)))=
v(u(f(x)))=

Question

If u(x)=4x-5, v(x)=x^2, and f(x)=1/x, find formulas for,
u(v(f(x)))=
u(f(v(x)))=
v(u(f(x)))=

anonymous · Answer

So, 
u(v(f(x)))=
4x-5(x^2(1/x(x)))?

stamp · Answer

u(v(f(x))=$$\frac{4}{x^2}-5$$

anonymous · Answer

how did you get that?

stamp · Answer

$$v(f(x))=(\frac{1}{x})^2$$

stamp · Answer

$$=\frac{1}{x^2}$$

anonymous · Answer

oh I was just plugging in the u and v I thought it needs to be solved.

anonymous · Answer

I did check and the answer in the back of the book and the answer you gave is right, but I am confused how you got it.

anonymous · Answer

Actually all I did was 
u(v(f(x)))=
plug the u, v, and f, 4x-5(x^2(1/x(x)))? I didn't really know from here if I was doing it right.

stamp · Answer

$$u=4x-5,\ v=x^2,\ f=1/x$$$$u(v(f)),\ v(f)=(1/x)^2,\ u(1/x^2)=4(1/x^2)-5$$$$u(v(f))=4/x^2-5$$

anonymous · Answer

thanks @stamp that's clear