Question 592791: Please help and show work. Thanks in advance.
a. Does the function f(x)=x^2 have an inverse? If so, what is it? If not, why not?
b. the function f(x)= x+3/x-5 has an inverse. Please find it.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Please help and show work. Thanks in advance.
a. Does the function f(x)=x^2 have an inverse? If so, what is it? If not, why not?
b. the function f(x)= x+3/x-5 has an inverse. Please find it.
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The method used to find the inverse: interchange x and y, then solve for y.
symbol used for inverse: y^-1
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a. y=x^2
This function does not have an inverse. If you graph this function, you will see that is is a parabola that opens upwards so for a given y you will have two different x's. This means it is not a one-to-one function and cannot have an inverse. You can also use the horizontal line test to show it will have two intersections which means the function is not one-to-one
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b. y=(x+3)/(x-5)
This function is one-to-one and its inverse can be found by interchanging x and y, then solving for y.
x=(y+3)/(y-5)
xy-5x=y+3
xy-y=5x+3
y(x-1)=5x+3
y^-1=(5x+3)/(x-1)
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