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:
$6.79
Step-by-step explanation:
We need to find the cost of a bottle of soap. We divide the cost by the number of bottles
$9.12/6 = $1.52 per bottle
We also need to find the cost for a sponge
$5.00/4 = $1.25 per sponge
We want to find the total cost of 2 bottles of soap and 3 sponges
cost = 2 * 1.52 + 3 * 1.25
= 3.04 + 3.75
= 6.79
Answer:
Step-by-step explanation:
→ Find the LCM of the denominators (2,4 and 8)
LCM = 8
→ Multiply the whole equation by 8 to get rid of the fractions
4x + 6 = 7
→ Minus 6 from both sides to isolate 4x
4x = 1
→ Divide both sides by 4 to isolate x
Hey!
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First Equation:
2x + 3 = -7
2x + 3 - 3 = -7 - 3 (Subtract 7 to both sides)
2x = -10
2x/2 = -10/2 (Divide 2 to both sides)
x = -5
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Second Equation:
4.5x - 7 = 20
4.5x + (-7) + 7 = 20 + 7 (Add 7 to both sides)
4.5x = 27
4.5x/4.5 = 27/4.5 (Divide 4.5 to both sides)
x = 6
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Third Equation:
-3x + 7 = 28
-3x + 7 - 7 = 28 - 7 (Subtract 7 to both sides)
-3x/-3 = 21/-3 (Divide -3 to both sides)
x = -7
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Answers:
2x + 3 = -7 → x = -5
4.5x - 7 = 20 → x = 6
-3x + 7 = 28 → x = -7
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Hope This Helped! Good Luck!
8x - 9y = 11 (subtract 8x from each side)
- 9y = -8x + 11 (divide -9 from each side)
y =
D. 
