Question

Noah's cousin is exactly 7 years younger than Noah. Let C represent Noah's cousin age and N represent Noah's age. Age is measured in years.

1. Write a function that defines the cousins age as a function of Noah's age.

2. What variable represents the input of this function?

3. What variable represents the output of this function?

4. Write the inverse of the function you wrote.

5. What variable represents the input of the inverse function?

6. What represents the output of the inverse function?​

Answer 1

1. f(N) = C ,where C = N - 7

2. The input of the function is x = N

3. The output of the function = y = C = N -7

4. F(C) = N where N = C - 7

5. Input of the inverse function = C

6. Output of the inverse function = N = C - 7

Explanation:

Let Noah's cousin age = C

and Noah's age = N

As given ,Noah's cousin is exactly 7 years younger than Noah.

⇒ C = N - 7

a.)

As we know that , A function is a maping of x to y such that f(x) = y

Let x = N , y = C

So, f( x) = y

⇒f(N) = C ,where C = N - 7

b.)

The input of the function is x = N

c.)

The output of the function = y = C = N -7

d.)

A inverse function is a mapping of y to x

i.e change the variable ,

As we have C = N - 7

It becomes

N = C - 7

So the inverse function becomes

F(C) = N where N = C - 7

e.)

Input of the inverse function = C

f.)

Output of the inverse function = N = C - 7