Question

Consider this function.

h(x) = (x - 2)^2+3

Which of the following domain restrictions would enable h(x) to have an inverse function?
a. x < 1
b. x ＞5
c. x < 3
d. x > 4

(Ps: all four answer and larger equal then or smaller equal then

Answer 1

No inverse function: (a), (b), (c)

Inverse function exists: (d)

Explanation:

The graph of h(x) = (x - 2)^2 + 3 is a parabola that opens upward and has vertex at (2, 3). If the entire graph is drawn, and the horizontal line test then applied, h(x) would not have an inverse, because the horizontal line would intersect the parabolic graph twice.

Note that if we restricted the domain to x ≥ 2, the resulting graph would pass the horizontal line test. This would also be true for x ≥ 3, x ≥ 4, and so on. Not so for (a) x < 1. False for x > -5. True for x < 3. True for x > 4.

No inverse function: (a), (b), (c)

Inverse function exists: (d)