Question

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?

Answer 1

Answer:

(a) f(36)=390

(b) $b=69$

(c) $f^{-1}(x)=\frac{750-x}{10}$

(d) After 35 months.

(e)$c=150$

Step-by-step explanation:

The given function is

$f(x)=750-10x$

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.

$f(36)=750-10(36)$

$f(36)=750-360$

$f(36)=390$

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.

$f(b)=750-10b$

$60=750-10b$

$60-750=-10b$

$-690=-10b$

$69=b$

Therefore, the value of b is 69.

(c)

Find inverse of the function.

$f(x)=750-10x$

Substitute f(x)=y.

$y=750-10x$

Interchange x and y.

$x=750-10y$

Isolate y.

$y=\frac{750-x}{10}$

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

$f^{-1}(x)=\frac{750-x}{10}$

(d)

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

$f(x)<400$

$750-10x<400$

$-10x<400-750$

$-10x<-350$

Divide both sides by -10.

$x>35$

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

(e)

The meaning of c in $f^{-1}(c)=60$ is the value of computer after 60 months.

From part (c)we have

$f^{-1}(x)=\frac{750-x}{10}$

$f^{-1}(c)=\frac{750-c}{10}$

$60=\frac{750-c}{10}$

$600=750-c$

$c=750-600$

$c=150$

Therefore, the value of c is 150.