Question

The amount of fuel remaining in a gas grill is a function of the number of hours, h that the grill has been used. This relationship can be expressed by the function below. F(h) = 100 - 2h Determine and represent the domain of this function for the problem situation using inequality notation.

Answer 1

Given:

The amount of fuel remaining in a gas grill is a function of the number of hours.

$F(h)=100-2h$

To find:

The domain for this situation.

Solution:

Domain is the set of input values.

The amount of fuel remaining in a gas grill F(h) is

$F(h)=100-2h$

where, h is the number of hours.

Here, domain is the set of all possible values of h.

We know that, time and remaining fuel cannot be negative. So,

$h\geq 0$      ...(i)

$F(h)\geq 0$

$100-2h\geq 0$

$100\geq 2h$

$50\geq h$       ...(ii)

Using (i) and (ii), we get

$0\leq h\leq 50$

Therefore, the domain of the given function is $0\leq h\leq 50$.