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How to find the value of an inverse function?

In this example, we are given f(x) = square root of (x2 - 9) and x is in the range of less than and equal to negative three. The question asks for f-1(4). How to find the value of the inverse function? The independent variable of the function f is x and its range is x <= -3. The independent variable of the inverse function f-1 is y. So, the question is asked for when y = 4, what is the corresponding value of x? We start from y = square root of (x2 - 9). Substitute y = 4 into the equation. So, 4 = square root of (x2 - 9). Now square booth side of the equation, we get 16 = x2 - 9. Simplify it, x2 = 16 + 9 = 25. Then x1 = 5 and x2 = -5. Since we are given x <= -3, so x1 = 5 is not in the range of x, so x1 = 5 should be drop. So, x = -5. That is, when y is 4, x is -5.