An inverse undoes a one-to-one function by swapping inputs and outputs.
WHAT HAPPENS IF…If f(x)=2x+1, which input does the inverse send 3 to?
Interactive exploration
Loading the mathematical model…
Connect the picture to the ideaf(x)=ax+b,f−1(y)=ay−b(a=0)
Solve y=ax+b for x. The inverse sends the output y back to the original x. Every point (x,y) on the forward graph becomes (y,x) on the inverse graph. This family uses a positive, nonzero slope, so it is one-to-one.
A detail that matters
The notation f⁻¹ denotes the inverse function here, not the reciprocal 1/f.