Question

True or False?
Picture provide below

Answer 1

Choice A is correct.The function is continuous at x=2.The given statement is true.

Explanation:

We have given a piece-wise function.

We have to find is it is continuous at x=2?

The function is f(x) = -2x+4 if x<= 2

Put x= 2 in the above function we get,

f(2) = -2(2)+4 = 0

So, the function is continuous at x=2 , when x<=2.

Now, when x > 2 the given function is f(x) = 2x-4 so, this function is also continuous.

Thus, the function is continuous at x=2. then given statement is true.

Answer 2

Option 1. It's True.

Explanation:

In this question given function is f(x) = -2x + 4 if x ≤ 2

Now if we put x = 2 in the given function then we get the value of this function

f(2) = 0 . So this function is continuous at x = 2.

and for the second condition

f(x) = 2x - 4 if x > 2 the given function is continuous.

Therefore we can say that given function is continuous at x = 2 is a true statement.