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Hello,
Can I get feedback on if these look correct?
1 Given f = { (-1, 8), (3, -1), (-2, 0) } and g = { (-5, 8), (3, -1), (-1, 0) } . Find (f o g)(3). Show steps,
( f o g)(3) = f ( g(3) ) = f(-1) = 3 (IS THIS CORRECT?)
2 Given f = { (-1, 8), (3, -1), (-2, 0) } and g = { (-5, 8), (3, -1), (-1, 0) } . Find (g o f)(3). Show steps,
( g o f)(3) = g ( f(3) ) = g(-1) = 3 (IS THIS CORRECT?)
5 f(x) = 15x -12 and g(x) = -15x^2 + 14x - 10, find (f o g)(-1).
( f o g)(-1) = f ( g(-1) )
g(-1) = -15^2 + 14(-1) - 10 = -249
f(-249) = 15(-249) - 12 = -3747
(f o g)(-1) = -3747 (FOR THIS ONE I WAS TOLD THAT -15 IS NOT SQUARED, BUT IN THE G FUNCTION IT IS SQUARED. WHAT AM I SUPPOSED TO CHANGE?)
Is it supposed to be done like this:
(f o g)(-1) = f( g(x))
f( -15^2 + 14x - 10)
15x ( -15^2 + 14x - 10) - 12
-3375x + 210x^2 -150x - 12
= 210^2 -3525x - 12
6 f(x) = -13x2 -13x + 14 and g(x) = -13x - 11, find (g(g(-3)).
(g o g)(-3) = g ( g(-3))
= g ( (-13x - 11) )
= -13 (-13x - 11) -11
= -169x + 143 - 11
= 169x + 132 (THE FEEDBACK WAS THAT FIRST, g(-3)) PUT -3 IN THE G FUNCTION AND THEN SIMPLIFY)
Is it supposed to go like this:
(g o g)(-3) = g ( g(-3))
g(-3) = -13(-3) -11 = 28
(g o g)(-3) = 28
7 f(x) = 2x + 3 and g(x) = –x^2 + 5, find (g o g)(x).
(g o g)(x) = g (g(x))
= g (-x^2 + 5)
= √(-x^2 + 5)
= -x + 5 Domain: {x:x Є R} (I WAS TOLD THAT THE RADICAL SHOULDN'T BE THERE. HOW DO I SOLVE THIS?)
8 f(x) = x + 3 and g(x) = √x, find g(f(x)).
(g o f)(x) = g ( f(x))
= g (x + 3)
= √(x + 3) Domain: {x: x ≤ 3} (IS THIS CORRECT?)
9 f(x) = x - 1 and g(x) = 3/(x-1), find f(g(x)).
(f o g)(x) = f (g(x))
= f [ 3/ (x - 1) ] Domain: {x: x ≥ 1} (IS THIS CORRECT?)
FOR THE FOLLOWING EXERCISE I HAVE SOLVED PARTS A AND B, BUT AM TOLD THAT THE ANSWER FOR PART C IS NOT ENOUGH.
10 You go to a local mechanic to get your tires changed. The tires cost x dollars. There is a 6% sales tax, but you get a 10% discount.
A Write a function t(x) for the total purchase amount after taxes but before discounts and fees.
Function with no discount and fees:
tax: 6%
tire cost: x
t(x) = x + 6% of x
t(x) = x + 0.06x
t(x) = 1.06x
B Write a function d(x) for the total after discounts on purchase amount x but before taxes and fees.
Function with no taxes and fees:
When discount is given after tax, then 10% is deducted from the original cost of the tire:
d(x) = x - 0.10x
C Does it make a difference in the total price whether the mechanic adds the tax first d(t(x)) or takes the discount first t(d(x))? Do not replace x with a numerical value. Show the work to support your answer while keeping x in your work.
It does make a difference in the total price if discount is applied first. Out of the whole amount, you would pay 90% of what it costs. When taxes are added to the discounted price, then the total price would be way less than if the taxes were added first and then the discount.
Thank you so much,
Jade
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