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
f(8,000)=15,000+1.5*8,000=15,000+ 12,000=27,000 (dollars)
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:
y=15,000+1.5x
1.5x = y-15,000
X=y-15,000/1.5
thus, in functional notation, x, the monthly income, is a function , say g, of variable y, the max amount:
X=g(y) y-15000/1.5
since we generally use the letter x for the variable of a function, we write g again as:
G (x) x-15000/1.5
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
G(600,000)=60,000-15,000/ 1.5=45,000/1.5 =30,000
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
Answer:
Step-by-step explanation:
4unity to the left
3unity down
F(x)=x^3+2
we see the power is odd
the ends go in opsoite directions
we know that if the leadind coefient (number in front of highest power term) is positive, then odd powered polynomials go from bottom left to top right
and for even ones, it goes both up
for negative, odd ones go from top left to bottom right
for even, both go down
we gots
f(x)=1x^3+2
positive and odd, so it goes from bottom left to top right
as x approaches negative inifnity, y approaches negaitve infinity
as x approaches infinity, y approaches infinity
Answer:
60
Step-by-step explanation:
7x+30+9x+42=104
16x+72=104
16x=104-72
16x=32
x=2
SO:
<BOC=9x+42=
9(2)+42=
18+42=
60
