Abc electric uses this formula, f(x) = 750 − 10x, to depreciate computers, where f is the value of a computer and
x is the number of months since its purchase.
a. calculate f(36). what is the meaning of f(36)?
b. what is the meaning of b in f(b) = 60? what is the value of b?
c. write a formula for f^−1, and explain what it means in this situation.
d. when will the depreciated value of a computer be less than $400?
e. what is the meaning of c in f−1(c) = 60? what is the value of c?

(a) f(36)=390

(b)

(c)

(d) After 35 months.

(e)

Step-by-step explanation:

The given function is

where f is the value of a computer and x is the number of months since its purchase.

(a)

Substitute x=36 in the given function.

It means the value of a computer is 390 after 36 months since its purchase.

(b)

It is given that f(b)=60. It means the value of a computer is 60 after b months since its purchase.

Therefore, the value of b is 69.

(c)

Find inverse of the function.

Substitute f(x)=y.

Interchange x and y.

Isolate y.

Here, y represents the number of months after which the value of the computer is $x.

(d)

The depreciated value of a computer be less than $400. It means

Divide both sides by -10.

After 35 months, the depreciated value of a computer be less than $400.

(e)

The meaning of c in is the value of computer after 60 months.

From part (c)we have

Therefore, the value of c is 150.