Question

What is the domain of the function f (x) = StartFraction x + 1 Over x squared minus 6 x + 8 EndFraction? all real numbers all real numbers except –1 all real numbers except –4 and –2 all real numbers except 2 and 4

Answer 1

Option D is correct.

The domain of the function f(x) is all real numbers except 2 and 4.

Explanation:

f(x) = (x+1)/(x²-6x+8)

The domain of a function expresses the region of values of x, where the function exists.

And logically, a function exists where ever f(x) has a finite value. That is, the only point where A function does not exist is when f(x) gives infinity.

For a rational function, the point where a function doesn't exist is when the denominator of the rational function is equal to 0. Because (numerator/0) --> ∞

So, the denominator in this question is

x²-6x+8

The function doesn't exist when

x²-6x+8 = 0

So, we solve the quadratic equation that ensues to get the values of x where the function doesn't exist.

x²-6x+8 = 0

x² - 4x - 2x + 8 = 0

x(x-4) - 2(x-4) = 0

(x-2)(x-4) = 0

(x-2) = 0 or (x-4) = 0

x = 2 or x = 4

This means that the function doesnt exist at x = 2 and x = 4

Indicating further that the function exists everywhere except at x = 2 and x = 4.

Hence, from the definition of domain given above, it is clear that the domain of the given function is all real numbers except 2 and 4.

Hope this Helps!!!

Answer 2

all real numbers except 2 and 4

Explanation:

The exceptions in the domain are the values that make the denominator zero. For a denominator of x² -6x +8 = (x -4)(x -2), the values that make it zero are x=4 and x=2.

The domain is all real numbers except 2 and 4.