Question

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

Answer 1

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=(u-2)/(5)`

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

`f(u)=(2((u-2)/(5))-1 )/((u-2)/(5) )` and of course that mess needs to be simplified:

`f(u)=((2u-4)/(5)-1 )/((u-2)/(5) )` and

`f(u)=((2u-4)/(5)-(5)/(5) )/((u-2)/(5) )` and

`f(u)=((2u-4-5)/(5) )/((u-2)/(5) )` and

`f(u)=((2u-9)/(5) )/((u-2)/(5) )` and bring up the lower fraction and flip it to multiply to get

`f(u)=(2u-9)/(u-2)` and now we can change the u to an x to get that

`f(x)=(2x-9)/(x-2)`