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:
32 gallons of water
Step-by-step explanation:
8 minutes = 480 seconds.
set up a proportion:
1/15=x/480
we have to solve for x:
15x=480
x=32.
Jess uses 32 gallons of water.
Answer:
I think its 25 (proceed with caution)
Step-by-step explanation:
15×4=60 so basically 6.25×4=25
6.25 = 6 1/4
It is 1 because a penny is worth 1 cent.
Answer:
y - 7 = 
(x + 8)
Step-by-step explanation:
Use the slope formula 
to work out the slope
Then pick one point to insert into the formula y - y1 = m(x - x1)
