If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ
-$$f ( x ) = \sqrt { x - 3 } , x \geq 3$$
A) $f ^ { - 1 } ( x ) = \sqrt { x + 3 }$
B) $f ^ { - 1 } ( x ) = x ^ { 2 } + 3 , x \geq 0$
C) not a one-to-one
D) $f ^ { - 1 } ( x ) = ( x - 3 ) ^ { 2 }$

Question

Quizplus · Accepted Answer

Given $f(x) = \sqrt{x - 3}, x \geq 3$, the function is one-to-one because it passes the horizontal line test (each output is unique to one input). To find the inverse, swap $x$ and $y$, then solve for $y$: $x = \sqrt{y - 3}$ leads to $x^2 = y - 3$, so $y = x^2 + 3$, with the condition $x \geq 0$ because the original function's domain starts at 3, and its range is non-negative.

If the Function Is One-To-One, Find Its Inverse f(x)=x−3,x≥3f ( x ) = \sqrt { x - 3 } , x \geq 3f(x)=x−3​,x≥3

If the Function Is One-To-One, Find Its Inverse $f ( x ) = \sqrt { x - 3 } , x \geq 3$