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Is an inverse of a linear equation always a function?

Updated: 4/28/2022
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Preciousdog92

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15y ago

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NO!!! As a matter of fact, unless the function is a one-to-one function, where each x in the domain has one and only one image in the range and no y in the range is the image of more than one x, then it won't ever be a function after being inversed. Just remember to switch the x's and y's with each other and then solve for y to get the inverse. If you don't believe me, then use then graph the function and then its inverse and do the vertical line test on both.

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Q: Is an inverse of a linear equation always a function?
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Related questions

Is the inverse of a linear function not a function?

The inverse of a linear function is always a linear function. There are a few ways to approach this.To think about it, you can imagine flipping the x and y axes. Essentially this equates to turning the graph of the linear function on its side to reveal the new inverse function which is still a straight line.More rigorously, the linear function y = ax + b has the inverse equation x = (1/a)y - (b/a). This is a linear function in y.


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Linear equations are always functions.


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No a linear equation are not the same as a linear function. The linear function is written as Ax+By=C. The linear equation is f{x}=m+b.


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No a linear equation are not the same as a linear function. The linear function is written as Ax+By=C. The linear equation is f{x}=m+b.


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The derivative of a quadratic function is always linear (e.g. the rate of change of a quadratic increases or decreases linearly).


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No. A function need not be linear. For example, y = sin(x) is a function of x but it is not a linear equation.


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There is one form of linear equation that is not a function, and that is when x = c, where c is a constant.


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