Question

The spending limit on johns credit card is given by the function f(x)=15000+1.5x, where x is his monthly income. F^-1 (x) = __ . The variable x represents _ In the inverse function. If johns spending limit is $60,00, his monthly income is _

Answer 1

to solve

f(x)=15000+1.5x

replace f(x) with y
switch x and y
solve for y
replace y with f⁻¹(x)

f(x)=15000+1.5x

replce f(x) with y

y=15000+1.5x

switch x and y

x=15000+1.5y

solve for y

y=(x-15000)/1.5

f-1(x) = (x-15000)/1.5

The variable x represents the spending limit on johns credit card  In the inverse function.

If johns spending limit is $60000, his monthly income is (60000-15000)/1.5=$30000

 If johns spending limit is $60,00, his monthly income is (60-15000)/1.5= -$9960------ >the johns spending limit must be >$15000