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:
109r6
Step-by-step explanationi got it
Answer:
you have a fixed rate of $25, meaning you get a haircut, it's $25
ANY other service is an extra $15
So, let's make the equation...
y=15x+25
Now, to just get a haircut it's $25.
But, let's say you get a haircut+shampoo
It'd be..
y=15(1)+25
y=$40
Another one..
You get a haircut+shampoo+highlight
y=15(3)+25
y=$70
Answer:
I think 80
Step-by-step explanation:
100/15=6.66666667
12x6.67=80.4
84 because 36 x 2 =72 and then 1/3 of 36 is 12 and 12+72=84
