Do the axes change when graphing an inverse function?

Question

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#.

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Answer 1 · 2018-01-19T16:09:33

No, axes do not change.

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]}