How do you find the domain of #h( x ) = \sqrt { x ^ { 2} - 7x - 8}#?

1 Answer
Daniel L.
May 26, 2017

See explanation.

Explanation:

The given function has an expression under square root sign. A square root can only be calculated if the value under square root sign is positive or zero.

So to calculate the domain we have to solve the inequality:

#x^2-7x-8>=0#

#Delta = (-7)^2-4*1*(-8)#

#Delta = 49+32=81#

#sqrt(Delta)=9#

#x_1=(7-9)/2=-1#

#x_2=(7+9)/2=8#

graph{x^2-7x-8 [-5, 10, -40, 40]}

Fromm the graph we see that the function's value is positive for

#x in (-oo;-1> uu <8;+oo)#

So the above interval is the domain of #f(x)#

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