Solve the problem.
-$$f ( x ) = x ^ { 2 } - 8 ( x \geq 0 )$$
A) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } + 8 , \mathrm { x } \geq - 8$
B) $f ^ { - 1 } ( x ) = \sqrt { x + 8 } , x \geq - 8$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } - 8 } , \mathrm { x } \geq 8$
D) $f ^ { - 1 } ( x ) = \sqrt { x ^ { 2 } + 8 } , x \geq - 8$

Question

Quizplus · Accepted Answer

To find the inverse function, replace f(x) with y and solve for x in terms of y.
$$y=x^2-8$$
$$x^2=y+8$$
$$x=\pm\sqrt{y+8}$$
Since x is only defined as non-negative, the inverse function is:
$$f^{-1}(x)=\sqrt{x+8}, x\geq -8$$
Choice B matches this form, so it is the best choice.

Solve the Problem f(x)=x2−8(x≥0)f ( x ) = x ^ { 2 } - 8 ( x \geq 0 )f(x)=x2−8(x≥0)

Solve the Problem $f ( x ) = x ^ { 2 } - 8 ( x \geq 0 )$