Question

u1 assessment wchs
let $f(x)=2(x-5)^2+3$
for what restricted domain would $f(x)$ be invertible?
$x \square \square$ or $x \square \square$

Explanation:

Step1: Identify vertex of parabola

The function $f(x)=2(x-5)^2+3$ is a parabola in vertex form $a(x-h)^2+k$, where vertex is $(h,k)=(5,3)$.

Step2: Determine monotonic intervals

A parabola opens upward ($a=2>0$), so it decreases left of vertex, increases right of vertex.

Step3: Define invertible domains

A function is invertible if it is one-to-one (monotonic). So restrict to $x \geq 5$ (increasing) or $x \leq 5$ (decreasing).

Answer:

$x \geq 5$ OR $x \leq 5$