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

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Answer 1 · 2018-08-02T04:40:25

#" "#
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:

enter image source here

Hope it helps.