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 find the inverse function of John's spending limit function, we solve for y in terms of x and then substitute $60,000 as the spending limit into the inverse function to find that John's monthly income is $30,000.

Step-by-step explanation:

The question asks to find the inverse function of f(x) = 15000 + 1.5x and to determine John's monthly income if his spending limit on his credit card is $60,000. To find the inverse function, we solve for x in terms of y, with y = f(x):

1. Replace f(x) with y: y = 15000 + 1.5x.
2. Swap x and y: x = 15000 + 1.5y.
3. Solve for y: y = (x - 15000) / 1.5.

The inverse function is f-1(x) = (x - 15000) / 1.5. In the inverse function, the variable x represents John's spending limit on the credit card.

If John's spending limit is $60,000, we substitute this value into the inverse function to find his monthly income:

y = (60000 - 15000) / 1.5 = 45000 / 1.5 = 30000

Therefore, John's monthly income is $30,000.

Answer 2

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