Question #4fbab

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Answer 1 · 2017-03-16T20:04:47

The domain of #f(x)# is #x < -4 and x > 3#

Because the argument for the #1/2# power cannot be negative we must find the part of the domain where #x^2+x-12>=0# and exclude it.

Let's find the points where the argument is 0:

#x^2+x-12=0#

Factor:

#(x +4)(x-3)=0#

This implies that:

#x+4=0 and x-3=0#

#x=-4 and x=3#

The function is negative between these values of x:

graph{x^2+x-12 [-8, 8, -14, 14]}

Therefore, the domain of #f(x)# is #x < -4 and x > 3#