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:714
Step-by-step explanation:
Answer:
The image is sideways.
But if your graph is like on the image, then the answer is: {y│-3 ≤ y ≤ 4}
Range is the set of y values
Least function value is -3 and greatest is 4
Answer: If the 40% off coupon is used, the subtotal will be $12.69
The gratuity would be exactly $4.23 (He will probably leave $4.25)
Step-by-step explanation: To find out the amount of the discount
.40 × 21.15 = 8.46
To find the new subtotal, subtract 12.15 - 8.46 = 12.69
To figure the tip: .20 × 21.15 = 4.23
Changing the percent to a decimal means divide the 20 by 100.
