Try plugging in the equations
and d are not it because they eliminate x
4x-12=3x-4
x=8
4x-12=6x-18
2x=6
x=3
so both b and c work as answers
Answer:
x = 1/2 and x = 9/2
Step-by-step explanation:
To solve this equation: |2x-5|=4 we need two evaluate two cases:
|2x-5| = 2x-5 when x>5/2 ✅
|2x-5| = -2x+5 when x<5/2✅
Then, if x>5/2:
2x-5 = 4 ➡ x = 9/2
Then, if x>5/2:
-2x+5 = 4 ➡ x = 1/2
Then, the two solutions are: x = 1/2 and x = 9/2
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.
===============================================
Problem 2
<h3>Answer: True</h3>
---------------------------------
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).
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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