Inverse of an absolute function

**Manni** · October 3rd 2011, 04:46 PM

Hey guys, just wondering how you would go about determining f^(-1) (x) of the function,

f(x) = x + |x|/2

What I did first was that I let f(x) = y. Then, I switched the x and the y variables

y = x + |x|/2

x = y + |y|/2

I don't know how to isolate for y since part of it is in absolute notation. Help?

**Wilmer** · October 3rd 2011, 04:50 PM

Math Forum - Ask Dr. Math

....googling does wonders...

**Manni** · October 3rd 2011, 04:57 PM

I still don't understand how I would apply it to the function I described, since it is partly an absolute value function.

**Plato** · October 3rd 2011, 05:20 PM

Originally Posted by Manni

Hey guys, just wondering how you would go about determining f^(-1) (x) of the function,

f(x) = x + |x|/2

Do you understand that any linear function $mx+b$ has an inverse?

Do you see that $x + \frac{{\left| x \right|}}{2} = \left\{ {\begin{array}{rl} {\dfrac{{3x}}{2},} & {x \geqslant 0} \\ {\dfrac{x}{2},} & {x < 0} \\ \end{array} } \right.$

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