What are the domain and range of the function f(x)=(√x-7)+9?

Mathematics

1 answer:

Yanka [14]3 years ago

3 0

Answer:

the domain of the function f(x) is $x\ge 7$

the range of the function f(x) is $f(x)\ge 9$

Step-by-step explanation:

Consider the parent function $y=\sqrt{x}.$

The domain og this function is $x\ge 0,$ the range of this function is $y\ge 0.$

The function $f(x)=\sqrt{x-7}+9$ is translated function $y=\sqrt{x}$ 7 units to the right and 9 units up, so

the domain of the function f(x) is $x\ge 7$

the range of the function f(x) is $f(x)\ge 9$

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at Michaels auto shop, it takes him 15 minutes to do an oil change and 24 minutes to do a tire change. let x be the number of oi

Roman55 [17]

Answer:

Step-by-step explanation:

At Susan's auto shop, it takes her 12 minutes to do an oil change and 18 minutes to do a tire change. Let x be the number of oil changes she does. Let y be the number of tire changes she does.

Using the values and variables given, write an inequality describing how many oil changes and tire changes Susan can do in less than 3 hours (180 minutes).

Answer provided by our tutors

The total time that Susan needs to change x oil changes and y tire changes is less than 180 min.

The time needed for x oil changes is 12 * x.

The time needed for y tire changes is 18 * y.

The total time is the sum of the above times and needs to be less than 180 that is

12 * x + 18 * y < 180 divide both sides of equation by 6

12/6 * x + 18/6*y < 180/6

2*x + 3*y < 30

2*x < 30 - 3*y divide both sides by 2 to get the inequality for x

x < 30/2 - 3/2*y = 15 - 1.5 y < 15 that is x < = 15

2*x + 3*y < 30

3*y < 30 - 2*x divide both sides by 3 to get the inequality for y