If the function is one-to-one, find its inverse. If not, write "not one-to-one."
-$$f ( x ) = \sqrt { x - 7 } , x \geq 7$$
A) $f ^ { - 1 } ( x ) = ( x - 7 ) ^ { 2 }$
B) not a one-to-one
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } + 7 , \mathrm { x } \geq 0$
D) $f ^ { - 1 } ( x ) = \sqrt { x + 7 }$

Question

Quizplus · Accepted Answer

Given $f(x) = \sqrt{x - 7}, x \geq 7$, the function is one-to-one because for each x-value there is exactly one y-value, and it passes the horizontal line test. To find the inverse, swap x and y and solve for y: $x = \sqrt{y - 7}$. Squaring both sides gives $x^2 = y - 7$, so $y = x^2 + 7$, with $x \geq 0$ because the original function's domain starts at 7, and after inversion, this affects the range of the inverse function.

If the Function Is One-To-One, Find Its Inverse f(x)=x−7,x≥7f ( x ) = \sqrt { x - 7 } , x \geq 7f(x)=x−7​,x≥7

If the Function Is One-To-One, Find Its Inverse $f ( x ) = \sqrt { x - 7 } , x \geq 7$