Explain, using the theorems, why the function is continuous at every number in i

Question

Explain, using the theorems, why the function is continuous at every number in its domain. M(x) = Squareroot 1 + 8/x M (x) is a polynomial, so it is continuous at every number in its domain. M (x) is a rational function, so it is continuous at every number in its domain. M (x) is a composition of functions that are continuous, so it is continuous at every number in its domain. M (x) is not continuous at every number in its domain. none of these State the domain. (Enter your answer using interval notation.) (- infinity, 0) Union (0, infinity)

Explanation / Answer

this one seem to be a little bit tricky for you

you thought that if x = 0 then the function is not defined which is correct .

but you forgot check the domain for the square root

for the square root to be defined , the function in the square root must be greater than or equal to 0

1+8/x >=0

8/x >= -1

x/8 <= -1

x <= -8 .

so domain = (-infinity ,8] U (0,infinity)

Hope this helps!!!

if you have any doubts just comment below

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