PLEASE ANSWER ASAP

Question

#1- Find the domain of the function: f(x)=sqrt(−5x+10)/(x^2−64)

 

#2- Find the domain of the function:
f(x)=−16sqrt(16x+20)+4sqrt(11−10x)

 

#3- Find the domain of the function:
f(x)=sqrt(3t−36)/(20+20t)

Answer 1

You know that the value under the square-root cannot be negative.  Also, the denominator can never be zero. 

 

1)

 

Assuming everything is under the square-root, set the following conditions:

 

-5x + 10 ≥ 0         or             x² - 64 > 0                1st case

 

 

                          and

 

 

-5x + 10 ≤ 0         or             x² - 64 < 0                 2nd case

 

 

 

Solving for the 1st case,    x ≤ 2          and           x < -8        or            x > 8

Solving for the 2nd case,   x ≥ 2          and           x > -8        and         x < 8

 

For the 1st case  domain to accept is  (-∞, -8)∪[2, 8)∪(8, ∞)

 

Work out the 2nd case. 

 

 

2)

 

Simply set the two arguments of the square-root greater than or equal to zero.

 

16x + 20 ≥ 0            and               11 - 10x ≥ 0

 

16x ≥ -20                                          -10x ≥ -11

 

x ≥ -1.25                                                x ≤ 1.1

 

 

Domain in interval [-1.25, 1.1).

 

 

Question 3 is the same as the first question.