Question

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

Answer 1

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)

Answer 2

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

Answer 3

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,
\[f ^{-1}(x)=(x+7)/5\]

Answer 4

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