+0  
 
0
76
1
avatar

Find the domain of the function \(\displaystyle f(x) = \sqrt{\ln \left(\frac {4x - x^2}3 \right)}\)

 Jun 10, 2020
 #1
avatar+21953 
0

Because both square roots and natural logs are not defined for negative values, let's find where the

function is zero.

 

sqrt[  ln[  (4x - x2) / 3 ] ]  =  0

--->   ln[  (4x - x2) / 3 ] ]  =  0                  (squaring both sides)

--->             (4x - x2) / 3  =  e0                (writing as an exponent)

--->              (4x - x2) / 3  =  1

--->                   (4x - x2)  =  3

--->              -x2 + 4x - 3  =  0

--->               x2 - 4x + 3  =  0

--->             (x - 1)(x - 3)  =  0

--->                      x = 1   or   x = 3

 

Checking values below 1 results in an undefined situation.

Checking values above 1 results in an undefined situation.

But, values  1 <= x <= 3  work so this is the domain.

 Jun 10, 2020

24 Online Users

avatar
avatar