Question

Find the x-values (if any) at which the function f(x)= =x^2-7x+3 is not continuous. Which of the discontinuities are removable? Find the x-values (if any) at which the function f(x)=(x-9)/(x^2-6x-27) is not continuous.

Answer 1

(1)

Step 1:

The function is .

The  function is in the form of quadratic function .

The domain of quadratic function defined for every value x.

The function has no undefined points nor domain constraints.

Therefore, The function is continuous over real numbers.

Solution:

The function is continuous for all values of .

Answer 2

(2)

Step 1:

The function is .

The domain of a function is all values of  , those makes the function mathematically correct.

Denominator of the function should not be the zero.

So, .

The function   is discontinuous at .

Answer 3

Contd....

Step 2:

The function .

Cancel common terms.

.

The discontinuity at is removable.

Solution:

The function  is discontinuous at .

Removable discontinuity is at .