hey besties i need help

Question

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Let

$f(x) = \begin{cases} k(x) &\text{if }x>2, \\ 2+(x-2)^2&\text{if }x\leq2. \end{cases}$

Find the function $k(x)$ such that $f$ is its own inverse.

wizzymath Mar 10, 2021

Guest · Answer 1 · 2021-03-21T09:47:16

Since we want k(x) to be its own inverse, k(x) = 2 + (x - 2)^2 = x^2 - 4x + 6.