$\text { Find } f ^ { t } ( x ) \text { if } f ( x ) = \log _ { 3 } \left( \frac { x ^ { 2 } - 5 } { x - 2 } \right)$
A)$f ^ { t } ( x ) = \frac { x ^ { 2 } - 2 } { x ^ { 2 } - 5 }$
B)$f ^ { t } ( x ) = - \frac { x ^ { 2 } - 2 } { \left( x ^ { 2 } - 5 \right) \ln ( 3 ) }$
C)$f ^ { t } ( x ) = \frac { x ^ { 2 } - 4 x + 5 } { \left( x ^ { 2 } - 5 \right) ( x - 2 ) \ln ( 3 ) }$
D)$f ^ { t } ( x ) = \frac { x ^ { 2 } - 4 x + 5 } { \left( x ^ { 2 } - 5 \right) ( x - 2 ) }$
E)$f ^ { t } ( x ) = \frac { x ^ { 2 } - 2 } { \left( x ^ { 2 } - 5 \right) \ln ( 3 ) }$

Question

$\text { Find } f ^ { t } ( x ) \text { if } f ( x ) = \log _ { 3 } \left( \frac { x ^ { 2 } - 5 } { x - 2 } \right)$ 
A)$f ^ { t } ( x ) = \frac { x ^ { 2 } - 2 } { x ^ { 2 } - 5 }$
B)$f ^ { t } ( x ) = - \frac { x ^ { 2 } - 2 } { \left( x ^ { 2 } - 5 \right) \ln ( 3 ) }$
C)$f ^ { t } ( x ) = \frac { x ^ { 2 } - 4 x + 5 } { \left( x ^ { 2 } - 5 \right) ( x - 2 ) \ln ( 3 ) }$
D)$f ^ { t } ( x ) = \frac { x ^ { 2 } - 4 x + 5 } { \left( x ^ { 2 } - 5 \right) ( x - 2 ) }$
E)$f ^ { t } ( x ) = \frac { x ^ { 2 } - 2 } { \left( x ^ { 2 } - 5 \right) \ln ( 3 ) }$

Quizplus · Accepted Answer

The derivative of $ f(x) = \log_3 \left( \frac{x^2 - 5}{x - 2} \right) $ is found using the chain rule and the derivative of the logarithm function. The correct derivative is $\frac{x^2 - 4x + 5}{(x^2 - 5)(x - 2) \ln(3)}$.

Find ft(x) if f(x)=log⁡3(x2−5x−2)\text { Find } f ^ { t } ( x ) \text { if } f ( x ) = \log _ { 3 } \left( \frac { x ^ { 2 } - 5 } { x - 2 } \right) Find ft(x) if f(x)=log3​(x−2x2−5​)

$\text { Find } f ^ { t } ( x ) \text { if } f ( x ) = \log _ { 3 } \left( \frac { x ^ { 2 } - 5 } { x - 2 } \right)$