Question

If f(2x)= 3x-1, find f(​

Answer 1

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

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

$f(x) =\frac{3x-2}{2}$  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) = $\frac{3(2x)-2}{2}$ and

$f(2x)=\frac{6x-2}{2}\\f(2x)=\frac{2(3x-1)}{2}\\f(2x)=3x-1$