# Find the domain algebraically: f(x)=sqrt(x^2-5x-14)?

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The function sqrt does not accept negative number.... Then to find the domain just solve the inequality... x^2 -5x -14 >=0 ... to solve this inequality, find the roots and study the signal.

Here the roots are x=- 2 and x = 7 .... The study of signal is

+ + + + + + + + + + (-2) - - - - - - - - - - - - -(7)+ ++ + + + + + + + + and the answer is the invervals

where the function is positive...

The domain is all real number x, so that: x<= -2 or x>= 7 OK!

• find the domain by finding the x values where y doesn't exist

you cant take the root of a negative number, so x^2-5x-14 must be positive

find where it changes from positive to negative by finding the roots

0=x^2-5x-14

0=(x-7)(x+2)

x= 7 or -2

test a number lower than -2, a number between -2 and 7, and a number higher than 7 to find where this graph is positive.

you will find that the graph is positive where x is less than -2, and where x is greater than 7. thats ur answer

• x^2 -5x -14 <0 (x-7)(x+2) <0 when -2 < x <7

domain : x can take any value <-2 or >7

• The argument of square root must be greater than or equal to 0. Write that inequality, that the quadratic is >= 0. Solve it the way you have been taught to solve quadratic inequalities.