Find the domain and range of the real function, defined by Show that f is many - one.
For domain (1 + x2)≠0
⇒x2≠ - 1
⇒dom(f) = R
For the range of x:
⇒
ymin = 0 (when x = 0)
ymax = 1 (when x = ∞)
∴range of f(x) = [0,1)
For many one the lines cut the curve in 2 equal valued points of y therefore the function f(x) is many - one.
Ans:
dom(f) = R
range(f) = [0,1)
function f(x) is many - one.