Find functions f and g so that f $f \circ g = H$
-$$H ( x ) = \frac { 6 } { \sqrt { 9 x + 10 } }$$
A) $f ( x ) = 6 ; \quad g ( x ) = \sqrt { 9 + 10 }$
B) $f ( x ) = \frac { 6 } { x } ; \quad g ( x ) = 9 x + 10$
C) $f ( x ) = \frac { 6 } { \sqrt { x } } ; \quad g ( x ) = 9 x + 10$
D) $f ( x ) = \sqrt { 9 x + 10 } ; g ( x ) = 6$

Question

Quizplus · Accepted Answer

Option C is correct because $g(x) = 9x + 10$ transforms the input $x$ into $9x + 10$, and then $f(x) = \frac{6}{\sqrt{x}}$ takes this result and applies the square root followed by division by 6, matching the given function $H(x) = \frac{6}{\sqrt{9x + 10}}$.

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

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