ABC Electric uses this formula, f(x) = 750 − 10x, to depreciate computers, where f is the value of a computer andx 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:(a) f(36)=390(b) [tex]b=69[/tex](c) [tex]f^{-1}(x)=\frac{750-x}{10}[/tex](d) After 35 months.(e)[tex]c=150[/tex]Step-by-step explanation:The given function is[tex]f(x)=750-10x[/tex]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.[tex]f(36)=750-10(36)[/tex][tex]f(36)=750-360[/tex][tex]f(36)=390[/tex]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.[tex]f(b)=750-10b[/tex][tex]60=750-10b[/tex][tex]60-750=-10b[/tex][tex]-690=-10b[/tex][tex]69=b[/tex]Therefore, the value of b is 69.(c)Find inverse of the function.[tex]f(x)=750-10x[/tex]Substitute f(x)=y.[tex]y=750-10x[/tex]Interchange x and y.[tex]x=750-10y[/tex]Isolate y.[tex]y=\frac{750-x}{10}[/tex]Here, y represents the number of months after which the value of the computer is $x.[tex]f^{-1}(x)=\frac{750-x}{10}[/tex](d)The depreciated value of a computer be less than $400. It means[tex]f(x)<400[/tex][tex]750-10x<400[/tex][tex]-10x<400-750[/tex][tex]-10x<-350[/tex]Divide both sides by -10.[tex]x>35[/tex]After 35 months, the depreciated value of a computer be less than $400.(e)The meaning of c in [tex]f^{-1}(c)=60[/tex] is the value of computer after 60 months.From part (c)we have[tex]f^{-1}(x)=\frac{750-x}{10}[/tex][tex]f^{-1}(c)=\frac{750-c}{10}[/tex][tex]60=\frac{750-c}{10}[/tex][tex]600=750-c[/tex][tex]c=750-600[/tex][tex]c=150[/tex]Therefore, the value of c is 150.