Pre calc

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Find the Domain of the function:
f(x)=the square root of the entire fraction- x^2+6x-16 over x^2-2x-15

  • Pre calc -

    domain is your choice of x's you can use

    First of all the bottom cannot be zero
    so
    x^2 - 2x - 15 ≠ 0
    (x-5)(x+3) ≠ 0
    x≠5 or x≠ -3

    Secondly the entire expression cannot be negative, because of the square root part

    it simplifies to
    (x+8)(x-2)/((x-5)(x+3)

    clearly any x<-8 and x> 5 are ok
    also the expression is positive between -3 and 2

    it is negative between -8 and -3, as well as 2 to 5

    I will let let you summarize the above.
    Make a number line , put those critical values on and mark the line accordingly

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