Restrict the domain of the following function $f$ so that the function is one-to-one and has an inverse function.
$$f ( x ) = - | x - 4 | + 2$$
A) $[ - 4 , \infty )$
B) $[ 2,4 ]$
C) $[ 4 , \infty )$
D) $[ - 2,4 ]$
E) $( - \infty , 2 ]$

Question

Quizplus · Accepted Answer

The function $f(x) = -|x - 4| + 2$ is symmetric about the vertical line $x = 4$, meaning it is not one-to-one over its entire domain. To make it one-to-one, we can restrict the domain to either side of the symmetry line. Choosing the interval $[4, \infty)$ ensures the function is one-to-one and can have an inverse, as it includes the vertex of the V-shaped graph and extends in one direction (to the right), avoiding the mirrored, non-one-to-one part of the graph to the left of $x = 4$.

Restrict the Domain of the Following Function fff So That the Function Is One-To-One and Has an Inverse

Restrict the Domain of the Following Function $f$ So That the Function Is One-To-One and Has an Inverse