Question

Do the axes change when graphing an inverse function?

For instance, if the original function is `d(t)=-2.8(t-5)^2 + 70` and the inverse function is `t(d)=sqrt(-1/2.8(d-70)) + 5`.

Answer 1

No, axes do not change.

Explanation:

No, axes do not change. A function `f(x)` and `f^(-1)(x)` are just the reflection of each other through line `y=x`.

For example, while `d(t)=-2.8(t-5)^2` appears as

graph{-2.8(x-5)^2+70 [-200, 200, -100, 100]}

while `t(d)=sqrt(-1/2.8(d-70))+5` appears as

graph{sqrt(-1/2.8(x-70))+5 [-200, 200, -100, 100]}

A part of the graph, however, is not appearing due to range limitations.

Now see the two graph together.

graph{(y+2.8(x-5)^2-70)(y-sqrt(-1/2.8(x-70))-5)(y-x)=0 [-200, 200, -100, 100]}