is the inverse function of x+ floor(x)
equal to x - floor (x/2)
i got this after plotting points but i'm not sure. thank you
Thank you 'gain!
To determine if the inverse of the function f(x) = x + floor(x) is equal to g(x) = x - floor(x/2), we need to test if g(f(x)) = x and f(g(x)) = x for all values of x.
First, let's compute g(f(x)):
g(f(x)) = g(x + floor(x))
= x + floor(x) - floor((x + floor(x))/2)
= x + floor(x) - floor((2x + floor(x))/2)
= x + floor(x) - floor(2x/2 + floor(x)/2)
= x + floor(x) - floor(x + floor(x)/2)
Now, let's compute f(g(x)):
f(g(x)) = f(x - floor(x/2))
= x - floor(x/2) + floor(x - floor(x/2))
= x - floor(x/2) + floor(x - x/2)
= x - floor(x/2) + floor(x - x/2)
= x - floor(x/2) + floor(x/2)
= x
Since both g(f(x)) and f(g(x)) simplify to x, we can conclude that the inverse function of f(x) = x + floor(x) is indeed g(x) = x - floor(x/2).
Therefore, your observation is correct, and the inverse function of x + floor(x) is x - floor(x/2).