SOLUTION: Find the inverse of the one-to-one function. f(x) = (x - 5)3 Group of answer choices

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Question 1179074: Find the inverse of the one-to-one function.
f(x) = (x - 5)3
Group of answer choices

Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Find the inverse of the one-to-one function.
f(x) = (x - 5)3
write as
y = 3(x-5)
swap x & y and solve for y
3(y-5) = x
y - 5 = x%2F3
y = x%2F3 + 5
write it
f%5E-1%28x%29 = x%2F3 + 5

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


I suspect the given function is supposed to be %28x-5%29%5E3 ("(x-5)^3") instead of %28x-5%293 ("(x-5)3")...

In typed text, it is standard to use "^" to denote exponentiation.

The standard method for finding the inverse of a function is to switch the x and y and solve for the new y:

y+=+%28x-5%29%5E3 --> x+=+%28y-5%29%5E3

Solve for y....

x+=+%28y-5%29%5E3
x%5E%281%2F3%29+=+y-5
y+=+x%5E%281%2F3%29%2B5

ANSWER: the inverse function is f%5E%28-1%29%28x%29+=+x%5E%281%2F3%29%2B5

For a relatively simple function like this, the inverse function can be found much faster using the idea that the inverse function "gets you back where you started" by performing the inverse operations in the opposite order. For this example, we have....

The given function (a) subtracts 5 and (b) cubes the result

The inverse function must (a) take the cube root and (b) add 5

ANSWER: The inverse function is x%5E%281%2F3%29%2B5