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).
Answer: y = (x + 5)² + 8
<u>Step-by-step explanation:</u>
y = x²
left 5 units: y = (x + 5)²
up 8 units: y = (x + 5)² + 8
Answer:
The right answer is:
The poll provides strong evidence that more than 61% of Americans oppose the Tea Party movement this year. Why? The P-value (0.026) is less than the significance level of 5%.
Step-by-step explanation:
At a level of significance of 5%, a P-value of 0.026 (2.6%) means that the difference is significant and the null hypothesis is rejected.
The difference between the proportions is significant, what means that more than 61% of Americans oppose the Tea Party movement this year.
Note: The difference in the sample proportions (3%) is not enough to claim that the difference is significant.
The right answer is:
The poll provides strong evidence that more than 61% of Americans oppose the Tea Party movement this year. Why? The P-value (0.026) is less than the significance level of 5%.
I’m not to sure I was wondering the same thing
84= 7(6+a)
84= 42 +7a
84-42= 42-42 +7a
42= 7a
42/7= 7a/7
6= a
-84= -6( p+6)
-84= -6p -36
-84+36= -6p -36+36
-48= -6p
-48/-6= -6p/-6
8 =p
