SOLUTION: If f(x) = (x - 2)^1/3, then f^-1(x) = a. (x3 + 1)/2 b. (x3 - 1)/2 c. (x3 + 2)/2 d. (x3 - 2)/2 e. x3

SOLUTION: If f(x) = (x - 2)^1/3, then f^-1(x) = a. (x3 + 1)/2 b. (x3 - 1)/2 c. (x3 + 2)/2 d. (x3 - 2)/2 e. x3 - 2 f. x3 + 2 g. none of these

Question 51040: If f(x) = (x - 2)^1/3, then f^-1(x) =
a. (x3 + 1)/2
b. (x3 - 1)/2
c. (x3 + 2)/2
d. (x3 - 2)/2
e. x3 - 2
f. x3 + 2
g. none of these
Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
f(x) = (x - 2)^1/3, then f^-1(x) =?
----------------
y=(x-2)^(1/3)
Interchange x and y to get:
x=(y-2)^(1/3)
Solve for y as follows:
Raise both sides to the 3rd power to get:
x^3=y-2
y=x^3+2
That is the inverse function.
Cheers,
Stan H.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
If , find
First, replace f(x) with y, so now you have:
Cube both sides.
Interchange the variables.
Now solve for y.
Finally, replace y with
This is choice f. in your list.
Check:
= = x
= = x
The above check is based on the following:
f(x) and g(x) are inverses of each other iff:
f(g(x)) = x for all x in the domain of g, and g(f(x)) = x for all x in the domain of f.
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