SOLUTION: I need help with two questions please. 1. Find the inverse of the one-to-one function f)x) = (x - 2)^3. 2. The function f(x) = (x + 1)/(2x - 1) is a one-to-one function. Wh

Algebra ->  Functions -> SOLUTION: I need help with two questions please. 1. Find the inverse of the one-to-one function f)x) = (x - 2)^3. 2. The function f(x) = (x + 1)/(2x - 1) is a one-to-one function. Wh      Log On


   

Question 324697: I need help with two questions please.
1. Find the inverse of the one-to-one function f)x) = (x - 2)^3.
2. The function f(x) = (x + 1)/(2x - 1) is a one-to-one function. What is the range of f^1(x)?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Next time, one question per post. Why should I do two problems and only get credit for one?

1.

Replace with



Solve for in terms of





Swap the positions of the variables and replace with



Can also be expressed:



Done.

2. Use the procedure above to determine that the inverse of the given function is:



Zero of the denominator is . When from the left, , but when from the right, .

Since the numerator and denominator polynomials are of the same degree, the rational function is asymptotic to the ratio of the lead coefficients, namely in this case. Hence, is excluded from the range.

Range, in interval notation:

Range, in set builder notation:

John