Question

If f(x)=x^2-1 what is the equation for f^-1(x)

Answer 1

Answer:

see below

Step-by-step explanation:

Swap y and x, then solve for y.

Original:

... y = f(x) = x² -1

Swap y and x:

... x = y² -1

Add 1:

... x + 1 = y²

Take the square root:

... ±√(x+1) = y . . . . . matches the 3rd selection

Rewrite as the inverse relation: (not a function)

... f^-1(x) = ±√(x+1)

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Comment on the graph

The attached graph shows the function f(x) in red, and the inverse relation g(x) in blue. You will note that g(x) is double-valued for most values of x, so is not a function. The function and its inverse relation are mirror images of each other in the line y=x. (That is, swapping y and x changes the function to its inverse, and vice versa.)