Answer:
B. 3x² – 10x + 13
Step-by-step explanation:
given:
f(x) = 3x² – 8x + 5
g(x) = 2x – 8
f(x) - g(x)
= (3x² – 8x + 5) - (2x – 8)
= 3x² – 8x + 5 - 2x + 8
= 3x² – 10x + 13
Company B; the ratios of cost to weight are equivalent.
Step-by-step explanation:
Step 1:
In the equation, 
k is the constant of proportionality.
If the values are in accordance with , the values of k will be constant for all the values.
So we determine the values of k for both the companies and see which has a constant k.
If 
. In these tables, y is the total cost and x is the weight in lbs.
Step 2:
For company A,
when 
when 
when 
For company B,
when 
when 
when 
So company B has a constant value of 
.
Problem 1
<h3>Answer: False</h3>
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Explanation:
The notation (f o g)(x) means f( g(x) ). Here g(x) is the inner function.
So,
f(x) = x+1
f( g(x) ) = g(x) + 1 .... replace every x with g(x)
f( g(x) ) = 6x+1 ... plug in g(x) = 6x
(f o g)(x) = 6x+1
Now let's flip things around
g(x) = 6x
g( f(x) ) = 6*( f(x) ) .... replace every x with f(x)
g( f(x) ) = 6(x+1) .... plug in f(x) = x+1
g( f(x) ) = 6x+6
(g o f)(x) = 6x+6
This shows that (f o g)(x) = (g o f)(x) is a false equation for the given f(x) and g(x) functions.
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Problem 2
<h3>Answer: True</h3>
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Explanation:
Let's say that g(x) produced a number that wasn't in the domain of f(x). This would mean that f( g(x) ) would be undefined.
For example, let
f(x) = 1/(x+2)
g(x) = -2
The g(x) function will always produce the output -2 regardless of what the input x is. Feeding that -2 output into f(x) leads to 1/(x+2) = 1/(-2+2) = 1/0 which is undefined.
So it's important that the outputs of g(x) line up with the domain of f(x). Outputs of g(x) must be valid inputs of f(x).
-15 so that is negative. so that is negative 15÷15 so 15 ÷15 is 1 so it would be -15÷-15=-1
