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How do you find the domain of #f(x) = 2(x-3)^2+1#?

Answer 1

Savannah Anderson

#" "#
Domain of the function

#color(red)(f(x) = 2(x-3)^2+1# is given by

#color(blue)((-oo < x < oo)#

In interval notation: #color(blue)((-oo,oo)#

#" "#
Given:

#color(red)(f(x) = 2(x-3)^2+1#

Domain is the set of all input values that generate the output values for the function.

For the values, the function is defined.

There are no values that makes the function undefined.

Hence,

Solution:

#color(blue)((-oo < x < oo)#

In interval notation:

#color(blue)((-oo,oo)#

We can examine the graph below to verify:

Hope it helps.

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Answer 2

Abigail Allen

To find the domain of ( f(x) = 2(x-3)^2 + 1 ), you need to identify any values of ( x ) that would result in undefined expressions within the function. Since ( (x-3)^2 ) can be squared for any real number ( x ), the only potential issue is if the expression inside the square root becomes negative. However, since ( (x-3)^2 ) always results in a non-negative value, there are no restrictions on the domain. Therefore, the domain of ( f(x) ) is all real numbers, or ( (-\infty, +\infty) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.