Question

only answer interval of increase or decrease and equation of asymptote

Answer 1

Solution

Given the function

$f(x)=-\log\lbrack-(x-5)\rbrack+4$

Domain

setting -(x - 5)>0

=> x - 5 < 0

=> x < 5

$D=\lbrace x\text{ \mid}x<5\rbrace$

Taking the derivative of f(x) with respect to x

$\begin{gathered} f^{\prime}(x)=-\frac{1}{(x-5)\ln10} \\ \\ \text{ setting }f^{\prime}(x)=0 \\ \\ \text{ The critical point is }x=5\text{ since }f^{\prime}(5)\text{ is undefined.} \end{gathered}$

Hence the interval of Decrease is

$(-\infty,5)$

The equation of asymptote is x =5