Math Interactive
2. Functions
2.2. Inverse functions
2.2.2. Domain and range
Important

As ff and f−1f^{-1} are “opposites” of each other, we have the following formulas for the domain and range of f−1f^{-1}.

Df−1=Rf.{D_{f^{-1}} = R_f.}
Rf−1=Df.{R_{f^{-1}} = D_f.}

Visualization

f(x){f(x)}
x{x}
f{f}
Df{\boxed{D_{f}}}
Rf{\boxed{R_{f}}}
x{x}
f−1(x){f^{-1}(x)}
f−1{f^{-1}}
Rf−1{\boxed{R_{f^{-1}}}}
Df−1{\boxed{D_{f^{-1}}}}

The diagrams help visualize what functions and inverse functions do, as well as provide a justification for the range and domain formulas above.

Next: Formula >>