Question

If f(2x)= 3x-1, find f(​

Answer 1

Explanation:

I'm assuming that you're looking for f(x) here given that f(2x) = 3x - 1.

The key is to make a substitution for f(2x) so things are easier for us in the long run. Let u = 2x. Now solve that for x so x is in terms of u:

x = u/2. Therefore, f(2x) becomes f(u) and

`f(u)=3((u)/(2))-1\\f(u)=(3u)/(2)-1\\f(u)=(3u)/(2)-(2)/(2)\\f(u)=(3u-2)/(2)`and now we can replace the u with the x (to put it back in terms of x):

`f(x) =(3x-2)/(2)` We can check our work by using that and evaluating it at f(2x). If we are right, then f(2x) = 3x - 1.

f(2x) =
`(3(2x)-2)/(2)` and

`f(2x)=(6x-2)/(2)\\f(2x)=(2(3x-1))/(2)\\f(2x)=3x-1`