Question

Determine all numbers at which the function is continuous.
Picture provided below

Answer 1

Choice C is correct.Function is continuous at all numbers except x=5 and x= 9.

Explanation:

We have given a piece-wise function.

We have to find all numbers at which the function is continuous.

f(x) = (x²-7x+10)/(x²-14x+14)

The function is not continuous when the denominator of function is zero.

So, function is continuous at all numbers except the values of x for which the denominator is zero.

First, factorize the term in the denominator of function we get,

f(x) = (x²-7x+10)/(x-5)(x-9)

The function is not continuous when (x-5)(x-9) = 0.

(x-5)(x-9) =0

Either x-5 = 0 or x-9 = 0

x = 5 or x = 9.

So, function is continuous at all numbers except x=5 and x= 9.

Answer 2

Option C. continuous except x = 5 and x = 9.

Explanation:

The given function is
`f(x)=(x^(2)-7x+10)/(x^(2)-14x+45)`

Now we have to check the continuity of the given function

We know if the denominator of a function which is in the form of a fraction is 0 then the given function is not continuous.

If we put x - 5 = 0

x = 5

and x - 9 = 0

x = 9

These are the two values of x for which the function is not defined.

Therefore option C. function is continuous except x = 5 and x = 9

is the correct answer.