Find f^ −1. f(x) = \/```` <-- this is suppose to be like the check mark and straight line over the equation?
so here is the equation
f(x)=\/```x-7 ,x>7
^ this first part the \/``` goes over the whole entire x-7 i hope you understand what I mean..
I need to get f^-1(x)=
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Do you not know that √(x-7) is the square root of (x-7)?
Standard procedure: replace f(x) on the left with x; replace x with f^-1 on the right; solve for f^-1:
x = √(f^-1 - 7)
x² = f^-1 - 7
x² + 7 = f^-1
The range of f is the domain of f^-1, so the domain of f^-1 is x > 0.
Try it: let x = 8; then f(8) = √(8-7) = √1 = 1. f^-1(1) = 1² + 7 = 8
No proof by any means that this is right, but if you hadn't got back the original x-value (8 in this case) that would have signaled that something was wrong in the calculation.