If f(x) = 5x - 7, what is f -1(x)?

Question

whpalmer4 · Answer

To find the inverse, set $$y=f(x)$$and solve for $x$.  Then rewrite the equation, swapping $x$ and $y$.  The result is $f^{-1}(x)$.

To check your work, graph both $f(x)$ and $f^{-1}(x)$.  They will appear identical except reflected across a 45 degree line through the origin (y=x)

whpalmer4 · Answer

Here's an example graph of a function and its inverse

anonymous · Answer

If you apply what whpalmer4 said,
$$y=5x-7$$
Add 7 to both sides,
$$5x=y+7$$
Divide by 5,
$$x=(y+7)/5$$
Switch the variables,
$$f ^{-1}(x)=(x+7)/5$$

whpalmer4 · Answer

Yep, that's what I got as well.  As the answer has been revealed, here's the graph: