Andre says 10x + 6 and 5x + 11 are equivalent because they both equal 16 when x is 1. Do you agree with Andre?
1 answer:
Answer:
No, They are not equivalent
Step-by-step explanation:
The two expressions are only said to be equivalent if they are the same regardless of whatever value the variable(s) is.
The variable in this question is x.
To prove this, we equate both expressions:
This shows that they have the same value ONLY when x is 1.
This is why Andre says that they are equivalent, but they are not.
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<h3>Answer: Choice (b)</h3><h3>{ (1, 3), (3, 1), (4, 3) }</h3>
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Work Shown:
The notation "g o f" means g(f(x)). We have f(x) as the inner function that is computed first.
f(x) = { (1,2), (3,5), (4,1) }
The x coordinates of each point are: 1, 3, 4
The y coordinates are: 2, 5, 1
So the input x = 1 goes to y = 2 as the output. That output becomes the input of the g(x) function. Using x = 2 as the input for g, we see that 3 is the output. Check out the diagram below to see how each input goes into f, then goes into g to ultimately determine the x,y pairs. So far we've shown that x = 1 ultimately leads to y = 3.
Let's do another input: if x = 3 is plugged into f(x), then the output is 5 because of the point (3,5). Then x = 5 is plugged into g(x) to get x = 5 lead to y = 1. Ultimately x = 3 leads to y = 1 giving us (3,1) as another point.
Lastly, if x = 4 is plugged into f we get y = 1 as an output, which in turn is plugged into g to get 3 as the final output. The point (4,3) is the last ordered pair.
Again there's a lot to keep track of, so it helps to have a diagram as shown below.