Answer:
The common continuous interval will be (0,∞).
Step-by-step explanation:
Given that,
The numerator = 12+√x
The denominator = √12+x
We know that,
For the numerator,
Any function under square root should be greater than and equal to the zero.
[tex]x\geq 0[/tex]
So, the continuous interval is (0, ∞)
For the denominator,
[tex]\sqrt{12+x}>0[/tex]
[tex]12+x>0[/tex]
[tex]x>-12[/tex]
The interval for the continuous and non zero function is,
(-12, ∞)
We need to calculate the continuous interval
Using given quotient
[tex]\dfrac{12+\sqrt{x}}{\sqrt{12+x}}[/tex]
The continuous interval of numerator and denominator are (0, ∞) and (-12, ∞).
Hence, The common continuous interval will be (0,∞).