Functions f(x)

Question

determine the choice value for f(-2) that will make the function f(x) continuus at x=-2 for the domain (-infinity to -2) U( -2 to infinity) 

 

original function was f(x)= x^2-4/x+2

Answer 1

f(x) = (x²-4) / (x+2) = (x-2)(x+2) / (x+2)

 

                               = x-2, for all x ≠ -2

 

The graph of f is a straight line with a hole at the point (-2,-4).

 

Defining f(-2) to equal -4 fills in the hole and makes the function continuous.