The domain of the expression sqrt(36-4x^2)

Question

 Find the interval ___ _________ , ___ ________

Answer 1

√(36 - 4x²) is defined only when 36 - 4x²≥ 0

 

                                                (6-2x)(6+2x)≥0

 

(6-2x)(6+2x) = 0 when x = 3 or -3

 

__________l__________l_______________

                 -3                3

 

When x < -3, 6-2x > 0 and 6+2x < 0

 

          So, (6-2x)(6+2x) < 0

 

When -3 < x < 3, 6-2x > 0 and 6+2x >0

 

          So, (6-2x)(6+2x) > 0

 

When x > 3, 6-2x < 0 and 6+2x > 0

 

          So, (6-2x)(6+2x) < 0

 

Domain:  [-3, 3]