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stepladder [879]
3 years ago
9

Determine if the equation defines y as a function of x: 2xy=1

Mathematics
1 answer:
Leona [35]3 years ago
3 0
Solve for y...

2xy=1

y=1/(2x)

So this is a function as each x value (with the exception of x=0) produces just one value for y.  However, technically there is a vertical asymptote about the vertical line x=0.  So there is a discontinuity as x=0.

I say this technically, because most would say that this function is true even with the discontinuity (as they do with say y=tana), but technically the discontinuity makes this not a function because another requirement of a function is for their to be an actual output value for each input value.  In this case division by zero when x=0 is undefined and cannot be included as part of a function.  So if you are picky about being absolute, 2xy=1 is really two functions.  One with a domain of (-oo,0) and another with a domain of (0,+oo).
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3 years ago
Jim drove 605 miles in 11 hours. At the same rate, how many miles would he drive in 13 hours?
svlad2 [7]

Answer: 715 Miles


Step-by-step explanation:

Divide 605 miles by 11 hours, which would give you how far he travels in 1 hour. (605/11=55)  Since they give you 13 hours, multiply 13 hours by 55 miles which gets you 715 miles :)

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3 years ago
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Naddika [18.5K]

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Step-by-step explanation:

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8 0
3 years ago
Use the following function to find the value of each operation.
Murljashka [212]
<h2>Evaluating Composite Functions</h2><h3>Answer:</h3>

w(f(m(2))) = 593

<h3>Step-by-step explanation:</h3>

We can write how w(f(m(x))) will be defined but that's too much work and it's only useful when we are evaluating w(f(m(x))) with many inputs.

First let's solve for m(2) first. As you read through this answer, you'll get the idea of what I'm doing.

Given:

m(x) = -4x +1

Solving for m(2):

m(2) = -4(2) +1 \\ m(2) = -8 +1 \\ m(2) = -7

Now we can solve for f(m(2)), since m(2) = -7, f(m(2)) = f(-7).

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f(x)=3x-1

Solving for f(-7):

f(-7)=3(-7)-1 \\ f(-7) = -21 -1 \\ f(-7) = -22

Now we are can solve for w(-22). By now you should get the idea why w(f(m(2))) = w(-22).

Given:

w(x) = x^2 -5x -1

Solving for w(-22):

w(-22) = (-22)^2 -5(-22) -1 \\ w(-22) = 484 -5(-22) -1 \\ w(-22) = 484 +110 -1 \\ w(-22) = 593

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3 years ago
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Step-by-step explanation:

I hope this helps!

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