Help with inverses? I'm desperate here

Question

anonymous · Answer

$$f^-1(3) when f(x)=\frac{ 2x+3 }{ 5 }$$

anonymous · Answer

Please, I need help! This is the last question and I'd really like to know how to solve it!

anonymous · Answer

Basically let $$
3 = \frac{2x+3}{5}
$$Then solve for $x$.

anonymous · Answer

Okay, thank you. :) When does the inverse come in though? @wio

anonymous · Answer

Well, in the general case, you would let $$
y = \frac{2x+3}{5}
$$Then solve for $x$ to get something like $$
g(y) = x
$$Then $g(y)$ is basically the inverse function, and you can find any value of the inverse function by substituting it for $y$.

anonymous · Answer

In this case: $$
y = \frac{2x+3}{5} \
5y = 2x+3\
5y-3 = 2x\
\frac{5y-3}{2} = x
$$This is the inverse function.

anonymous · Answer

We could say $$
f^{-1}(x) = \frac{5x-3}{2}
$$

anonymous · Answer

Ohh, okay.  So we're basically just substituting values (: thank you, I have the general idea now