How do I find the inverse functions from abs(x^2 - 3)? WolframAlpha gives 4 expressions.

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- Nov 15th 2012, 04:44 AMStuck Maninverse functions
How do I find the inverse functions from abs(x^2 - 3)? WolframAlpha gives 4 expressions.

- Nov 15th 2012, 05:20 AMProve ItRe: inverse functions
This will not have an inverse function - it's not one-to-one... You could restrict the domain to get an inverse function though...

- Nov 15th 2012, 06:03 AMHallsofIvyRe: inverse functions
Yes, it does! And the reason is exactly what Prove It said- the function is not "one to one". If you were to graph it you would see that there are some horizontal lines that cross the graph 4 times- so 4 different values of x that give the same y value.

Specifically, is a parabola that crosses the x-axis at , goes down to (0, -3), back up to the x-axis at , and then up. Taking the absolute value then "folds" that portion below the x-axis up above it.

If , then so . Taking the absolute value of a positive number doesn't change it so, for , the function is . To find the inverse function, swap x and y and solve for y: so and . But in this case, y (which**was**x but got swapped) is less than or equal to -3. y is negative so .

If , then so . Taking the absolute value multiplies that by -1 so, for , . Again, we swap x and y and solve for y. so and . Because, here, x< 0 becomes y< 0, we must take the negative sign. .

If , we have the same situation as the previous case except that y is positive so we take the positive sign on the square root: .

If , we have the same situation as the first case except that y is positive so we take the positive sign on the square root: .