Wednesday

July 23, 2014

July 23, 2014

Posted by **Lynn** on Friday, March 28, 2008 at 5:20pm.

Problem

If f is one-to-one, find an equation for its inverse.

f(x)=x^3-5

y=x^3-5

x=y^3-5

5+x=y^3-5+5

5+x=y^3

My answer:

y^3=5+x

3y=35+x

y=35+x

f^-1(x)35+x

- Algebra Help Inverse One-to-one -
**Damon**, Friday, March 28, 2008 at 5:59pmy = (5+x)^(1/3)

is the easy way to write that.

Now lets say x = 3

then

y = 8^1/3 = 2

but what if y = (-1 + i sqrt 3)

square that

1 -2 i sqrt 3 - 3 = (-2 - 2i sqrt 3)

multiply that by (-1+ i sqrt 3)

2 -2 i sqrt 3 + 2 i sqrt 3 + 6

= 8 !!!!!

I also claim that the complex conjugate

y = (-1 -i sqrt 3)

cubed is also 8

therefore I claim that y = 2 or y = -1+i sqrt 3 or y = -1 -i sqrt 3

are all values of y for x = 3

So if your algebra subject is about complex as well as real numbers, there are three values of y for any value of x in the inverse problem.

- Algebra Help Inverse One-to-one -
**Lynn**, Friday, March 28, 2008 at 6:01pmSorry, my answer is:

y^3=5+x

3y=35+x

y=35+x

f^-1(x)=35+x

- Algebra Help Inverse One-to-one -
**Damon**, Friday, March 28, 2008 at 7:01pmbut whatever your symbol is for the cube root, you have to take the cube root of the whole right side, need parentheses

(5+x)

**Related Questions**

Algebra Help Inverse One-to-one - Did I do this right? Problem: If the ...

Pre-Calc - Does y=1/x have an inverse? It is a one-to-one function, so it should...

Algebra-One to one function - Could you please check my answers and help me with...

Algebra inverse - Find the formula for the inverse of each funtion. 3.) f(x)= 2x...

Math - Determine whether each equation is true for all x for which both sides of...

PreCalc! - sketch a graph whose domain is the interval [0, infinity) but whose ...

pre-calculus - the function f(x)=4/x-7 is one to one a. find the inverse of f b...

Algebra(1st one was typo) - The function f(x)=x^3 +1/4 x −1^4 is a ...

Trigonometry - I need help with the inverse of si, cos, & tan. So far on one ...

Algebra, Solving equations - I'm stuck with this equation: y = (4x-1)/(2x+3) We'...