7x^3-24x^2-19x+12
-----------------=f(x)
2x^3-4x^2-40x+80
Determine all values of x for which f is not defined.
2 answers
thats supposed to be a fraction all equel to f(x).
A function is not defined if the denominator is zero
So we just have to look at the bottom which I will assume is
2x^3 - 4x^2 - 40x + 80
by grouping
= 2x^2(x-2) - 40(x-2)
= (x-2)(2x^2 - 40)
so x-2 cannot be zero, or x ≠ 2
or
2x^ - 40 ≠ 0
x^2 ≠ 20
x ≠ ±√20 or ±2√5
so x ≠ 2, 2√5, -2√5
So we just have to look at the bottom which I will assume is
2x^3 - 4x^2 - 40x + 80
by grouping
= 2x^2(x-2) - 40(x-2)
= (x-2)(2x^2 - 40)
so x-2 cannot be zero, or x ≠ 2
or
2x^ - 40 ≠ 0
x^2 ≠ 20
x ≠ ±√20 or ±2√5
so x ≠ 2, 2√5, -2√5