What is the correct restriction of the graph f(x) = x^2-6x+15 to ensure that its inverse is also a function?
I'm not sure how to do this type of question, but I set y = x and solved and don't know how to continue.
2026-04-02 23:45:55.1775173555
Restrictions on inverse functions
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You can check to see if a function has an inverse through the "horizontal line test." Essentially, if you can draw a horizontal line that intersects your function more than once, your function does not have an inverse. Since this is a quadratic equation, you have to eliminate one "side" of the parabola. By the equation $\frac{-b}{2a}$ we know that the parabola's line of symmetry is at $x = \frac{6}{2} = 3$. Thus, your restriction can either be $(-\infty, 3]$ or $[3, \infty)$ You could also use a less general restriction such as $[3, 8]$ or $[-2, -1]$