Find functions f and g so that f $f \circ g = H$
-$$\mathrm { H } ( \mathrm { x } ) = \sqrt { \frac { 1 } { \mathrm { x } - 2 } }$$
A) $g ( x ) = \sqrt { x } ; f ( x ) = \frac { 1 } { x - 2 }$

B) $f ( x ) = x - 2 ; g ( x ) = \frac { 1 } { \sqrt { x } }$

C) $f ( x ) = \frac { 1 } { x - 2 } ; g ( x ) = \sqrt { x }$

D) $f ( x ) = \frac { 1 } { x - 2 } ; g ( x ) = \frac { 1 } { \sqrt { x } }$

Question

Find functions f and g so that f $f \circ g = H$
-$$\mathrm { H } ( \mathrm { x } ) = \sqrt { \frac { 1 } { \mathrm { x } - 2 } }$$
A) $g ( x ) = \sqrt { x } ; f ( x ) = \frac { 1 } { x - 2 }$

B) $f ( x ) = x - 2 ; g ( x ) = \frac { 1 } { \sqrt { x } }$

C) $f ( x ) = \frac { 1 } { x - 2 } ; g ( x ) = \sqrt { x }$

D) $f ( x ) = \frac { 1 } { x - 2 } ; g ( x ) = \frac { 1 } { \sqrt { x } }$

Quizplus · Accepted Answer

The correct functions are $f(x) = \frac{1}{x-2}$ and $g(x) = \sqrt{x}$ because when $g$ is applied first, it takes the square root of $x$, and then $f$ takes the result and computes $\frac{1}{\sqrt{x}-2}$, which matches the given $H(x)$ after recognizing that the input to $f$ is the output of $g$.

Find Functions F and G So That F f∘g=Hf \circ g = Hf∘g=H

Find Functions F and G So That F $f \circ g = H$