If f(x) = 245
Find f^-1(x) (the inverse)

9514 1404 393

  does not exist

Step-by-step explanation:

The notation f^-1(x) usually refers to the inverse function. That is, if we have the functional relation

  y = f(x)

Then the inverse function f^-1(x) will give you ...

  x = f^-1(y)

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In order for an inverse function to exist, the original function must pass the "horizontal line test." That is, any horizontal line can intersect the function's graph in, at most, one point.

Here, the function f(x) = 245 is a horizontal line, so the horizontal line test fails. The horizontal line at y=245 will intersect f(x) in an infinite number of points.

So, f(x) = 245 does not have an inverse function. f^-1(x) does not exist.

Alternate interpretation of the question

Sometimes, an exponent is applied to a function name when the intended operation is application of the exponent to the function value. For example, you may see sin²(x) when the intended meaning is sin(x)². The application of an exponent to the function name could be confused with multiple applications of the function: sin²(x) = sin(sin(x)), as the notation is sometimes used for this purpose, too.

If what you intend by f^-1(x) is really f(x)^-1, then you can say ...

  f(x)^-1 = 1/245