True or False, the inverse function and asymptotes of log functions

Question

(a) The inverse function of f(x) = log(x) is f^−1(x) =
1/ log(x) 

(b) If a and b are positive constants, then y = ln(ax + b) has no vertical asymptote

 

for A I am not sure but I think its false because if you switch x and y you get 10^x=y, but I'm not sure that is entirely right.

For B I really have no good guess. I would say true but I don't know.

Answer 1

Olivia,

 

graphing: Y = log x

 

 y-axis is vertical assymptote

 

 Point (1,0) is on graph

 

graphing: Y = log (X+ 1) translates the entire graph, including assymptote one unit right

 

Y = log (X - h) + k is graphing

                      form of equation

 

if h is negative, translate right

 

if h is positive, translate left

Answer 2

a)

 

False.  1 / log(x) would be the reciprocal of f(x).

 

 

b)

 

Lets say that a=1=b.

 

ln(x + 1)

 

 

A vertical asymptote would occur when x≤-1  in this case.

 

 

Answer is false.