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Pre Cal

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find the domains of the following functions:
a) f(x)=x^20
b) g(x)=1/(x-3)
c) h(x)=1/(4x^2=21x-18)
d) k(x)=sqrt (4x^2-21x-18)
e) p(x)=1/sqrt(4x^2-21x-18)

  • Pre Cal - ,

    a) -- anything goes
    b) -- anything except x=3
    c) we need factors of
    4x^2 - 21x - 18
    = (x - 6)(4x + 3)
    so x ≠6 or x ≠ -3/4

    d) Now the number inside the √ cannot be negative.
    so x ≤ -3/4 or x ≥ 6

    e) not the number inside cannot be zero or negative.
    you do that one, let me know what you got.

  • Pre Cal - ,

    isn't it the same as d, because the domain is looked at in the demoninatior?

  • Pre Cal - ,

    no,
    in d) the √ was a numerator while in e) it is now a denominator.
    So now we also have to worry about division by zero.

    btw, I just noticed a typo which probably caused confusion.
    e) should have said:

    " e) note that the number inside cannot be zero or negative. "

    Of course the result is zero when x=6 or x=-3/4, which we cannot have

    so just make it : x < 3/4 OR x> 6

  • Pre Cal - ,

    and x<3/4 or x>6 is the answer?

  • Pre Cal - ,

    If you understood what I worked for you, you should have realized that I missed the negative sign in x<-3/4 as a typo.

    so .......

    x < -3/4 OR x > 6

  • Pre Cal - ,

    Oops. sorry i was distracted while writing and forgot to put the negitive.

  • Pre Cal - ,

    this is wrong

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