Homework Help: Pre Cal

Posted by Angela on Sunday, July 24, 2011 at 8:20pm.

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 - Reiny, Sunday, July 24, 2011 at 9:18pm
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 - Angela, Sunday, July 24, 2011 at 9:23pm
isn't it the same as d, because the domain is looked at in the demoninatior?
Pre Cal - Reiny, Sunday, July 24, 2011 at 9:30pm
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 - Angela, Sunday, July 24, 2011 at 9:32pm
and x<3/4 or x>6 is the answer?
Pre Cal - Reiny, Sunday, July 24, 2011 at 9:42pm
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 - Angela, Sunday, July 24, 2011 at 9:44pm
Oops. sorry i was distracted while writing and forgot to put the negitive.
Pre Cal - Dalidah, Tuesday, August 16, 2011 at 4:54pm
this is wrong

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