Question

If fog(x)=2x-1/x and g(x)=5x+2 , find f(x).​

Answer 1

Answer:

Step-by-step explanation:

To do this, we will use a u substitution. Namely, let 5x + 2 = u and solve for x so u is in terms of x, since we have x in our composition.

5x + 2 = u, then

5x = u - 2 and

$x=\frac{u-2}{5}$

which changes f(g(x)) into f(u) {since g(x) = 5x + 2 = u}:

$f(u)=\frac{2(\frac{u-2}{5})-1 }{\frac{u-2}{5} }$ and of course that mess needs to be simplified:

$f(u)=\frac{\frac{2u-4}{5}-1 }{\frac{u-2}{5} }$ and

$f(u)=\frac{\frac{2u-4}{5}-\frac{5}{5} }{\frac{u-2}{5} }$ and

$f(u)=\frac{\frac{2u-4-5}{5} }{\frac{u-2}{5} }$ and

$f(u)=\frac{\frac{2u-9}{5} }{\frac{u-2}{5} }$ and bring up the lower fraction and flip it to multiply to get

$f(u)=\frac{2u-9}{u-2}$ and now we can change the u to an x to get that

$f(x)=\frac{2x-9}{x-2}$