1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Troyanec [42]
2 years ago
12

The spending limit on John’s credit card is given by the function f(x)=15,000+1.5x , where x is his monthly income. f^-1x . The

variable x represents in the inverse function. If John's spending limit is $60,000, his monthly income is .
Mathematics
1 answer:
Katena32 [7]2 years ago
6 0
<span>1.
"The spending limit on John’s credit card is given by the function f(x)=15,000+1.5x"

means that if the monthly income of John is $ 5,000 ,he can spend at most 

f(5,000)=15,000+1.5*5,000=15,000+ 7,500=22, 500 (dollars)

Or for example

if Johns monthly income is $8,000, then he can spend at most

 </span>f(8,000)=15,000+1.5*8,000=15,000+ 12,000=27,000 (dollars)<span>


2.
Now, assume that the maximum amount that John can spend is y.

Then, y=15,000+1.5x

we can express x, the monthly income, in terms of y by isolating x:

</span>y=15,000+1.5x
<span>
1.5x = y-15,000


</span>x= \frac{y-15,000}{1.5}
<span>
thus, in functional notation, x, the monthly income, is a function , say g, of variable y, the max amount:

</span>x=g(y)=\frac{y-15,000}{1.5}

since we generally use the letter x for the variable of a function, we write g again as:

g(x)=\frac{x-15,000}{1.5}
<span>
for example :

</span>g(50,000)=\frac{50,000-15,000}{1.5}= \frac{35,000}{1.5}= 23,333
<span>
tells us that if the maximum amount that John can spend is 50,000 $, then his monthly income is 23,333 $.

3.

If John's limit is $60,000, his monthly income is 

</span>g(60,000)=\frac{60,000-15,000}{1.5}= \frac{45,000}{1.5}=30,000<span>
 dollars.


Answer: $ 30,000

Remark: g is called the inverse function of f, since it undoes what f does.

instead of g(x), we could use the notation </span>f ^{-1}(x)<span>



</span>
You might be interested in
62% of what number is 186
ra1l [238]

Answer:

300

Step-by-step explanation:

Let the number be X

62/100 × X = 186

X = 186 × 100/62

X = 300

7 0
3 years ago
Read 2 more answers
What is 102011 rounded to the nearest one thosand
Julli [10]

Answer:

102000

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
F(x)= 3x + 5
Valentin [98]

Step-by-step explanation:

(3x+5)-(4x²-2)-(x²-3x+1)

= 3x+5-4x²+2-x²+3x-1

=6x+6-5x²

=-5x²+6x+6

5 0
2 years ago
Multi-step linear inequalities
Natali5045456 [20]

Step-by-step explanation:

5y + 3 > -7y + 13

12y > 10

y > 10/12

y > 5/6

6 0
3 years ago
Answer to 3,4,5,6,7,8,9,10,11,12 !!
sineoko [7]
3. i=129; j=112
4.k=90;l=116;m=64;n=86
5.o=13;p=78;q=91
6.a=120;b=60;c=140
Can't see #7
You did 8 I believe
9.v=39;w=59;x=121
10.y=59;z=93
11.a=42;b=48;c=132
12.a=60;b=50;c=80;d=100
8 0
2 years ago
Other questions:
  • What's the answer to 9,10,11, and 12
    15·1 answer
  • What is fifteen percent of seventy dollars
    9·2 answers
  • Please help 7th grade math! Find the interest.
    8·1 answer
  • Please help if u can!!
    6·1 answer
  • A. 16.0<br> b. 25.0<br> c. 9.0<br> d. 17.3
    9·1 answer
  • The area of a rectangle is 2x*2-13x+12 and another area is 6x^2-13x+21, what is the combined area of both rectangles?
    5·1 answer
  • Help please :( and thanks!!!
    8·2 answers
  • I’m not understanding what to do here
    5·1 answer
  • Denise spent $3.45 on snacks every day for 11 days. What is the amount of money Denise spent on these snacks?
    12·2 answers
  • Below are the functions of y = |x| and y= |x| - 9 how are the functions related?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!