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.Com
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) (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. \ =\ (x\ -\ 2)^3)
Replace )
with 
^3)
Solve for 
in terms of
Swap the positions of the variables and replace with )
\ =\ x^{\frac{1}{3}}\ +\ 2)
Can also be expressed:
\ =\ \sqrt[\small{3}]{x}\ +\ 2)
Done.
2. Use the procedure above to determine that the inverse of the given function is:
\ =\ \frac{x\,+\,1}{2x\,-\,1})
Zero of the denominator is 
. When 
from the left, \ \rightarrow -\infty)
, but when from the right, \ \rightarrow \infty)
.
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:\ \small{\cup}\Large\ \left(\frac{1}{2},\,\infty\right))
Range, in set builder notation: 
John
RELATED QUESTIONS
Given the one-to-one function f(x) = x^{1/3} + 2, find the inverse... (answered by Fombitz)
Pleas help me find the inverse of the one-to-one function, and write the inverse in... (answered by josgarithmetic)
f(x)=6-3x^2,if x<0
find the inverse of the one to one function... (answered by MathLover1)
Given the one-to-one function f(x) =(x-2)^3,find the inverse function (answered by jim_thompson5910)
Find the inverse of the given one to one function f(x) = (x-1)/(x+2) Give the domain and... (answered by stanbon)
The function f(x)=7x+2/x-3, x≠3, is one-to-one. Find an equation for f^-1(x), the... (answered by ankor@dixie-net.com)
The one-to-one function f is defined below.
f(x)=9-x^3
Find f^-1(x), where f^-1 is the (answered by ikleyn)
My question is about inverse functions, didn't see an area to submit them. Anyway I was... (answered by rothauserc)
Please help need to find the inverse of f(x) = 1/2 * (sqrt x-2)... (answered by CubeyThePenguin)