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)
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.
isn't it the same as d, because the domain is looked at in the demoninatior?
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
and x<3/4 or x>6 is the answer?
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