<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>

<span>
thus, in functional notation, x, the monthly income, is a function , say
g, of variable y, the max amount:
</span>

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

<span>
for example :
</span>

<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>

<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>

<span>
</span>
Answer:
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Hello,
I note (a,b,c) the result of a quarters, b dimes and c pennies:
2 solutions:
106=( 3, 3, 1)=( 1, 8, 1)
106=( 0, 0, 106) but : 100= 0*25+ 0*10+ 100
106=( 0, 1, 96) but : 100= 0*25+ 1*10+ 90
106=( 0, 2, 86) but : 100= 0*25+ 2*10+ 80
106=( 0, 3, 76) but : 100= 0*25+ 3*10+ 70
106=( 0, 4, 66) but : 100= 0*25+ 4*10+ 60
106=( 0, 5, 56) but : 100= 0*25+ 5*10+ 50
106=( 0, 6, 46) but : 100= 0*25+ 6*10+ 40
106=( 0, 7, 36) but : 100= 0*25+ 7*10+ 30
106=( 0, 8, 26) but : 100= 0*25+ 8*10+ 20
106=( 0, 9, 16) but : 100= 0*25+ 9*10+ 10
106=( 0, 10, 6) but : 100= 0*25+ 10*10+ 0
106=( 1, 0, 81) but : 100= 1*25+ 0*10+ 75
106=( 1, 1, 71) but : 100= 1*25+ 1*10+ 65
106=( 1, 2, 61) but : 100= 1*25+ 2*10+ 55
106=( 1, 3, 51) but : 100= 1*25+ 3*10+ 45
106=( 1, 4, 41) but : 100= 1*25+ 4*10+ 35
106=( 1, 5, 31) but : 100= 1*25+ 5*10+ 25
106=( 1, 6, 21) but : 100= 1*25+ 6*10+ 15
106=( 1, 7, 11) but : 100= 1*25+ 7*10+ 5
106=( 1, 8, 1) is good
106=( 2, 0, 56) but : 100= 2*25+ 0*10+ 50
106=( 2, 1, 46) but : 100= 2*25+ 1*10+ 40
106=( 2, 2, 36) but : 100= 2*25+ 2*10+ 30
106=( 2, 3, 26) but : 100= 2*25+ 3*10+ 20
106=( 2, 4, 16) but : 100= 2*25+ 4*10+ 10
106=( 2, 5, 6) but : 100= 2*25+ 5*10+ 0
106=( 3, 0, 31) but : 100= 3*25+ 0*10+ 25
106=( 3, 1, 21) but : 100= 3*25+ 1*10+ 15
106=( 3, 2, 11) but : 100= 3*25+ 2*10+ 5
106=( 3, 3, 1) is good
106=( 4, 0, 6) but : 100= 4*25+ 0*10+ 0