Question

Show all work to identify the discontinuity and zero of the function f of x equals 4 x over quantity x squared minus 16

Answer 1

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:

$f(x) = \frac{4x}{x^2 - 16}$

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

$\frac{4(x)}{(x)^2 - 16}=0\\4x =0((x)^2 - 16)\\4x=0\\x=0$

So, zero of function is when x=0