How do you find the domain of #f(x)=sqrt(12 - 2x^2)#?

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Answer 1 · 2018-03-13T16:18:01

#[-sqrt(6),sqrt(6)]#

To find the domain of a function, we find all possible values of its input which give a defined function.

Here, we have #sqrt(12-2x^2)#

Since when #x<0# the function of #sqrt(x)# will be undefined, we say this function is defined when:

#12-2x^2>=0#

#6-x^2>=0#

#-x^2>=-6#

#x^2<=6#

#-sqrt(6)<=x<=sqrt(6)#

So #f(x)# is only defined when it is between #-sqrt(6)# and #sqrt(6)#. In interval notation, we write this as:

#[-sqrt(6),sqrt(6)]#