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match each function with corresponding restrictions to its domain when p(x) = 2x and q(x) = 2 x .

Recall that the domain of a function is the set of all x values of the function for which the function is defined.

Given that

and

Given that

For the function to be undefined, the denominator should be zero

i.e. 2x = 0 which means that x = 0

Thus, the domain of the function is all real values of x except 0.

Therefore, the restriction is x ≠ 0.

Given that

For the function to be undefined, the denominator should be zero

i.e.

For x = 2,

Also, for x = 1

Thus, the domain of the function is all real values of x except 1 and 2.

Therefore, the restriction is x ≠ 1, 2.

Given that

For the function to be undefined, the denominator should be zero

i.e.

For x = -2,

.

Thus, the domain of the function is all real values of x except -2.

Therefore, the restriction is x ≠ -2.

Given that

There is no value of x, for which the function is undefined.

Thus, the domain of the function is all real values of x.

Therefore, there is no restrictions to the domain of the function.

Given that

For the function to be undefined, the denominator should be zero

i.e.

Thus, the domain of the function is all real values of x except -1.

Therefore, the restriction is x ≠ -1.

the ratio of grapes to blueberries she should use is 12: 3

step-by-step explanation:

if mandie is making 15 cups of fruit salad, the ratio of grapes to blueberries she should use is 12: 3.

"a" determine whether sage found the correct quotient. show your work

step-by-step explanation: