Answer:
Sale Price = $34.8 (answer). This means the cost of the item to you is $34.8. You will pay $34.8 for a item with original price of $43.50 when discounted 20%. In this example, if you buy an item at $43.50 with 20% discount, you will pay 43.50 - 8.7 = 34.8 dollars.
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Answer:
for any point (x, y), that appears in one function, the point (y, x) must appear in the other function. for any point (x, y), that doesn't appear in one function, the point (y, x) must not appear in the other function.
so if you find any point that doesn't meet the above rules, you can prove that the functions are not inverses of each other.
to prove that they are inverses of each other, you need to check all points in the functions, and there is an infinity of them, so instead, you can write f(x) like this:
y = 3x - 5
solve for x:
y + 5 = 3x
x = (y + 5) / 3
swap x and y:
y = (x + 5) / 3
this is the same as g(x) which, therefore the functions are inverse of each other.
Plug in what we know:
Find the cube root of both sides:
![\sf~a=\sqrt[3]{2744}](https://tex.z-dn.net/?f=%5Csf~a%3D%5Csqrt%5B3%5D%7B2744%7D)
Simplify:
There are several ways in which we could answer this question. My choice is to actually solve the given quadratic equation, x^2 + 4x + 4 = 12.
Note that x^2 + 4x + 4 is a perfect square. Thus,
x^2 + 4x + 4 = 12 is the same as (x+2)^2 = 12, so that
x+2 = plus or minus √3*√4, or plus or minus 2√3.
Thus, the two real, unequal roots are
x = -2 + 2√3 and x = -2 - 2√3. These correspond to answer choices C and E.
