SOLUTION: 3+(x+2)^5 what is the inverse of this equation. what are the steps I should take to achieve the answer?

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Question 1132798: 3+(x+2)^5 what is the inverse of this equation. what are the steps I should take to achieve the answer?
Found 3 solutions by math_helper, greenestamps, Alan3354:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
The general steps are:
Let y = f(x), solve for x, then swap the roles of x and y (literally swap the letters) and you will have y = g(x) where g(x) is the inverse of f(x).

+y+=+3%2B%28x%2B2%29%5E5+
+y+-+3+=+%28x%2B2%29%5E5+
+root%285%2C%28y+-+3%29%29+=+%28x+%2B+2%29+
+%28root%285%2C%28y+-+3%29%29%29+-+2+=+x+

Inverse of +3%2B%28x%2B2%29%5E5+ is therefore:
++highlight%28+y+=+%28root%285%2C%28x-3%29%29%29+-+2+%29+

Check:
g(f(x)) = x should hold true if g(x) is the inverse of f(x):
Substitute +3%2B%28x%2B2%29%5E5+ for "x" in the answer given:
+%28root%285%2C%283%2B%28x%2B2%29%5E5%29-3%29%29+-+2+ =

+%28root%285%2C%28x%2B2%29%5E5%29%29-2+ =

++%28x%2B2%29-2+ =

+x+

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


For relatively simple functions, there is a way to find the inverse that is nearly always much faster than switching the x and y and solving for the new y.

The method is based on the general concept that an inverse function "gets you back where you started".

For an inverse function to get you back where you started, the operations it performs must be the opposite operations from what the function does, and in the reverse order.

In your example, the operations the function performs on the input value are
(1) add 2
(2) raise to the 5th power
(3) add 3

The opposite operations, in the opposite order, are
(1) subtract 3
(2) take the 5th root
(3) subtract 2

That gives you, as the inverse function,

y+=+%28x-3%29%5E%281%2F5%29-2

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
What equation?
Equations have equal signs.