Answer:
Discontinuity of function occurs when x = 4 or x = -4
zero of function is when x=0
Step-by-step explanation:
We are given:
[tex]f(x) = \frac{4x}{x^2 - 16}[/tex]
Discontinuity of the function occur when the denominator is equal to zero.
So, we need to find the values of x that makes the denominator zero.
The denominator is x^2 - 16
x^2 - 16 =0
x^2 = 16
x = ± 4
So, if the value of x = 4 or value of x=-4 then the function will be discontinuous.
Zero of the function i.e f(x)=0
So, Putting the function equal to zero and finding the value of x
[tex]\frac{4(x)}{(x)^2 - 16}=0\\4x =0((x)^2 - 16)\\4x=0\\x=0[/tex]
So, zero of function is when x=0
