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)))=

Answer 1

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

Answer 2

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

Answer 3

how did you get that?

Answer 4

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

Answer 5

\[=\frac{1}{x^2}\]

Answer 6

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

Answer 7

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.

Answer 8

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.

Answer 9

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

Answer 10

thanks @stamp that's clear