If f(x)=x^2-1 what is the equation for f^-1(x)
1 answer:
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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<em>Comment on the graph</em>
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.)
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