find the domains of the following functions:

Question

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)

Answer 1

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.

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

this is wrong