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Nyasha
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Homework Statement
Find the inverse of y=3x-(1/2x)
The Attempt at a Solution
y=(6x^2-1)/(2x)
x=(6y^2-1)/(2y)
2yx=(6y^2-1)
2yx-6y^2=-1
2y(x-3y)=-1
2y(x-3y)=-1
( I am stuck here how do l solve for "y")
I realize that this switching of x and y is how many (most?) books present this process,Nyasha said:Homework Statement
Find the inverse of y=3x-(1/2x)
The Attempt at a Solution
y=(6x^2-1)/(2x)
x=(6y^2-1)/(2y)
Nyasha said:2yx=(6y^2-1)
2yx-6y^2=-1
2y(x-3y)=-1
2y(x-3y)=-1
( I am stuck here how do l solve for "y")
Dick said:You've got 6y^2-2xy-1=0. That's a quadratic equation in y. Solve it the way you would any other quadratic equation ay^2+by+c=0. a=6, b=-2x c=-1.
HallsofIvy said:Then please tell us how you solved that quadratic equation without using the quadratic formula!
Dick said:2x*(3x-1/(2x))=6x^2-1, not 3x-1. Or was your problem really y=(3x-1)/(2x)?
Are you given some restriction on x (i.e., the domain of f(x) = 3x - 1/(2x)) ? Otherwise, as you have discovered, f(x) does not have an inverse (an inverse function must be single-valued!).Nyasha said:Homework Statement
Find the inverse of y=3x-(1/2x)
Unco said:Are you given some restriction on x (i.e., the domain of f(x) = 3x - 1/(2x)) ? Otherwise, as you have discovered, f(x) does not have an inverse (an inverse function must be single-valued!).
Dick said:Sure. Or you could have interchanged them first and solved for y. Either way.
The inverse of a function is a function that "undoes" the original function. In other words, if you input the output of the original function into the inverse function, you will get the original input.
To solve for y, we need to isolate it on one side of the equation. First, we can combine like terms on the right side to get y=2.5x. Then, we can divide both sides by 2.5 to get y=0.4x.
The domain of the inverse function will be the range of the original function. In this case, the range of y=3x-(1/2x) is all real numbers, so the domain of its inverse will also be all real numbers.
Yes, this function is one-to-one because for every input (x value), there is only one output (y value). This means there are no repeated outputs for different inputs, which is a requirement for a function to be one-to-one.
To graph the inverse, we can switch the x and y values of the original function and plot the points. This will result in a reflection of the original graph over the line y=x. Alternatively, we can use the inverse function to find the points of the inverse and plot them on the same graph as the original function.