Question

find f^-1(x) if f(x)=5x

Answer 1

Solve for "x" in terms of \(y\)

Answer 2

Start with the defining equation\[y=5x \leftarrow \rightarrow x=5y\]
Solve for y in the inverse equation

Answer 3

Remember that when f(x) sends x to y, f^-1(x) sends y to x.

Answer 4

So for the simpler equations, inverse functions are essentially the "opposite" operation

Answer 5

f^-1(x) is the notation for an 'inverse function'
so we could reword the question as,
'find the inverse of y=5x'

the steps to finding the inverse of a function is to swap x and y
y=5x
becomes
x=5y

now, make this equation in the form of y= (y equals) and you'll have the solution to the question, "find f^-1(x) if f(x)=5x" (just remember to change y to f^-1(x) for the very last step)