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).
Let
x-------> the number of game tokens purchased for a member of the arcade
y-------> the function of the yearly cost in dollars
we know that
the function y of the yearly cost in dollars is equal to
This is the equation of the line
using a graph tool
see the attached figure
<u>Statements</u>
<u>case a)</u> The slope of the function is $1.00
The statement is False
The slope of the function is equal to 
<u>case b)</u> The y-intercept of the function is $60
The statement is True
we know that
The y-intercept of the function is the value of the function when the value of x is equal to zero
so
for 
<u>case c)</u> The function can be represented by the equation y =(1/10)x + 60
The statement is True
The equation of the function is equal to
<u>case d)</u> The domain is all real numbers
The statement is False
The value of x cannot be negative, therefore the domain is the interval
[0,∞)
<u>case e)</u> The range is {y| y ≥ 60}
The statement is True
The range of the function is the interval-------> [60,∞)
see the attached figure
Step-by-step explanation:
1. No: angles add to more than 180 deg.
2. Yes: each side's length is between the sum and difference of the lengths of the other two sides.
3. No: not every side's length is between the sum and difference of the lengths of the other two sides.
4. Yes: for example, place the 50 deg angle between the two given sides. Another side will then make the triangle.
5. Yes: for example, use 3 cm as the short leg in a 30-60-90 right triangle.
Y = 2
slope = 0
hope it helps
