Suppose f (x) and g(x) are continuous functions with the known values:

Suppose f (x) and g(x) are continuous functions with the known values:
X 0 1 2 3 4
F(x) 9 6 4 2 0
G(x) -3 -5 -1 3 5
Answer the following
Evaluate lim(x-->1) [3f(x)-5g(x)]
Evaluate lim (x--->3) [x^2+g(f(x))]
Is it possible for g(x) = 0? Justify your answer.

If the function is continuous, then the limit is the image.

Then lim(x->1) [ 3f(x) - 5(g(x)] = 3(6) - 5(-5) = 43 OK!

Then lim(x->3) [ x^2 g(f(x))] = 9 g(f(3) = 9-1 = 8 OK!

The question " Is it possible for g(x) = 0?" must be clear. What you want to know that is possible?

Note: at x= 2 ==> g(2) = -1 a negative number....at x=3 ==> g(3) = 3 a positive number... As g(x) is a continuous function, then there exist a value of x , 2