Question

What is the discontinuity and zero of the function

Answer 1

The discontinuity are the point wherein the function is not defined. 
The zeros are the points wherein f(x)=0.
Computing the discontinuity points:
Set $x-1=0$ then the discontinuity point is at $x=1$.
Comptine the zeroes:
Set $3x^2+x-4=0$
Compute the discriminant: $1^2-4(3)(-4)=49=7^2.$
Then with quadratic formula we get the solutions:
$(-1-7)/6=-8/6\\(-1+7)/6=1$
The two zeros are $\dfrac{-8}{6},1$