For what value(s) of the constant a is the function f continuous everywhere?

Question

f(x)= {a(x^2-2a)        if x < 0

          a sqrt(x+4) -4  if x greater than or equal to 0

Answer 1

Step 1:

The function is .

If the function is continuous, then the left hand limit is equal to right hand limit.

Consider left hand limit,

Consider right hand limit,

Step 2:

Find the values of a.

Left hand limit is equal to right hand limit.

Multiply each side with negative one.

Apply zero product property.

and .

and .

The function is continuous for and .

Solution:

The function is continuous for and .