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

1 answer:

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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Step-by-step explanation:

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3 years ago

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tamaranim1 [39]

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$(6)\ \ \ f(x)=ax^2\ \ \ and\ \ \ f(2)=48\\.\ \ \ \Rightarrow\ \ 48=a\cdot2^2\ \ \Rightarrow\ \ a=48:4=12\ \ \Rightarrow\ \ f(x)=12x^2\ \Rightarrow\ \ Ans.\ C\\\\(7)\ \ \ inversely:\ \ \ f(x)= \frac{a}{x} \ \ \ and\ \ \ f(2)=4\\.\ \ \ \Rightarrow\ \ \ 4= \frac{a}{2} \ \ \ \Rightarrow\ \ \ a=4\cdot2=8\ \ \ \Rightarrow\ \ \ y= \frac{8}{x}\ \ \ \Rightarrow\ \ \ Ans.\ B$