Answer:
Step-by-step 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
[tex]f(u)=3(\frac{u}{2})-1\\f(u)=\frac{3u}{2}-1\\f(u)=\frac{3u}{2}-\frac{2}{2}\\f(u)=\frac{3u-2}{2}[/tex]and now we can replace the u with the x (to put it back in terms of x):
[tex]f(x) =\frac{3x-2}{2}[/tex] 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) = [tex]\frac{3(2x)-2}{2}[/tex] and
[tex]f(2x)=\frac{6x-2}{2}\\f(2x)=\frac{2(3x-1)}{2}\\f(2x)=3x-1[/tex]
