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Q: What is the inverse function of y equals x 3?

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The inverse is not a function because it fails the vertical line test.

Simply stated, the inverse of a function is a function where the variables are reversed. If you have a function f(x) = y, the inverse is denoted as f-1(y) = x. Examples: y=x+3 Inverse is x=y+3, or y=x-3 y=2x+5 Inverse is x=2y+5, or y=(x-5)/2

3

log5x

Assuming the domain and range are both the real numbers (or rationals): Yes, it is 1 to 1 Yes, it is onto and the inverse is x = (y-3)/4

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The inverse is not a function because it fails the vertical line test.

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Simply stated, the inverse of a function is a function where the variables are reversed. If you have a function f(x) = y, the inverse is denoted as f-1(y) = x. Examples: y=x+3 Inverse is x=y+3, or y=x-3 y=2x+5 Inverse is x=2y+5, or y=(x-5)/2

3

6

log5x

Because the inverse of a function is what happens when you replace x with y and y with x.

To find the inverse of a function, simply switch the variables x and y. So for the function y=7x+3, the inverse would be x=7y+3, or y=(x-3)/7.

Assuming the domain and range are both the real numbers (or rationals): Yes, it is 1 to 1 Yes, it is onto and the inverse is x = (y-3)/4

X squared is not an inverse function; it is a quadratic function.

square root of x/pi

A reciprocal function will flip the original function (reciprocal of 3/5 is 5/3). An inverse function will change the x's and y's of the original function (the inverse of x<4,y>8 is y<4, x>8). Whenever a function is reflected over the line y=x, the result is the inverse of that function. The y=x line starts at the origin (0,0) and has a positive slope of one. All an inverse does is flip the domain and range.