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Which of the following has an inverse that is also a function?

g(x)=2x-3
k(x)=-9x^2
f(x)=|x+2|
w(x)=-20

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Answer:

g(x)=2x-3 has an inverse that is also a function.

A function has an inverse if and only if it is a one-to-one function. A one-to-one function is a function where no two elements in the range of the function have the same image. If a function is one-to-one, then it will have a unique inverse.

To find the inverse of a function, you can switch the roles of x and y and solve for y. For g(x)=2x-3, the inverse is:

y = 2x-3

x = (y+3)/2

This is the inverse of g(x), and it is also a function because it is a one-to-one mapping.

k(x) = -9x^2 and f(x) = |x+2| are not one-to-one, so they do not have inverses that are also functions.

w(x) = -20 is a constant function, so it is not one-to-one and does not have an inverse that is a function.

User Fabian Braun
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