Thread: Finding the inverse of a function

Find the inverse of the function:

f(x) = (3/4) x^5 + 5

read "three-fourths x to the fifth plus 5"


Graphing my progress on my calculator as I go, the last point where I get an inverse is at

5^[sqrt] ((4/3)x - (20/3))
^(root with an index of 5)

If I am thinking correctly, you cannot have a root in the denominator, so I've been multiplying the whole thing above by

5^[sqrt](3^4)
^again, root with an index of 5

to get the fifth root out of the denominator, but this messes the whole equation up and it no longer mirrors the original function when I plug it into my graphing calculator. Is there some rule with roots about square roots that I am unaware of?

Help is much appreciated.

Originally Posted by happydino1

Find the inverse of the function:

f(x) = (3/4) x^5 + 5

read "three-fourths x to the fifth plus 5"


Graphing my progress on my calculator as I go, the last point where I get an inverse is at

5^[sqrt] ((4/3)x - (20/3))
^(root with an index of 5)

If I am thinking correctly, you cannot have a root in the denominator, so I've been multiplying the whole thing above by

5^[sqrt](3^4)
^again, root with an index of 5

to get the fifth root out of the denominator, but this messes the whole equation up and it no longer mirrors the original function when I plug it into my graphing calculator. Is there some rule with roots about square roots that I am unaware of?

Help is much appreciated.

Analytically to find the inverse of a function we switch the roles of x and y to get , then solve for y: . g(x) is our inverse function.

So


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-Dan