Question

Select the correct answer from each drop down menu

Answer 1

h(x) is the quotient of f(x) divided by g(x), given by (x^2 - 8x + 15) / (x - 3), and the domain of h(x) is all real numbers except x = 3.

h(x) is the quotient of f(x) divided by g(x). Given that f(x) = x^2 - 8x + 15 and g(x) = x - 3, we can find h(x) as follows:

h(x) = f(x) / g(x)

By performing the division, we find that h(x) simplifies to:

h(x) = (x^2 - 8x + 15) / (x - 3)

The domain of h(x) refers to the set of all possible input values for which h(x) is defined. In this case, the only restriction is that we cannot divide by zero.

To find the domain, we set the denominator (x - 3) equal to zero and solve for x:

x - 3 = 0

Adding 3 to both sides, we get:

x = 3

Therefore, the domain of h(x) is all real numbers except x = 3.

Answer 2

For this case we have the following functions:

`f (x) = x ^ 2-8x + 15\\g (x) = x-3`

We have to:

`h (x) = \frac {f (x)} {g (x)} = \frac {x ^ 2-8x + 15} {x-3} = \frac {(x-3) (x-5) } {(x-3)} = (x-5)`

We have that by definition, the domain of a function is given by all the values for which the function is defined. We have that h (x) ceases to be defined when the denominator is 0. That is:

`x-3 = 0\\x = 3`

Thus, the domain is given by:

(-infinity, 3) U (3, infinity)

Answer:

`h (x) = (x-5)`

Domain: (-infinity, 3) U (3, infinity)