Which statement could be used to explain why f(x) = 2x – 3 has an inverse relation that is a function?

1. The graph of f(x) passes the vertical line test.
2. f(x) is a one-to-one function.
3. The graph of the inverse of f(x) passes the horizontal line test.
4. f(x) is not a function.

The inverse of function y=2x-3 can be found by expressing the function in terms of y rather than x, therefore, y will be an independent function.

[tex]y=2x-3\\\\y+3=2x\\\\x=\dfrac{y+3}{2}[/tex]

Hence, the inverse of the function is [tex]x=\dfrac{y+3}{2}[/tex].

To verify the inverse of the function [tex]x=\dfrac{y+3}{2}[/tex], we will plot the graph of both function and inverse, if both the function is one-to-one the inverse is correct, therefore, it will pass both the test horizontal line test and vertical line test.

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Which statement could be used to explain why f(x) = 2x – 3 has an inverse relation that is a function? 1. The graph of f(x) passes the vertical line test. 2. f(x) is a one-to-one function. 3. The graph of the inverse of f(x) passes the horizontal line test. 4. f(x) is not a function.

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What is the inverse of the function?

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Which statement could be used to explain why f(x) = 2x – 3 has an inverse relation that is a function?

1. The graph of f(x) passes the vertical line test.
2. f(x) is a one-to-one function.
3. The graph of the inverse of f(x) passes the horizontal line test.
4. f(x) is not a function.