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Find the domain and range of the rea...

Find the domain and range of the real function defined by `f(x) = (x^(2))/((1+x^(2))`
Show that f is many -one

Text Solution

Verified by Experts

When x is real `1+x^(2) ne 0` .So dom (f) =R
`y=(x^(2))/((1+x^(2))) rArr x^(2) (1-y) =y rArr x= sqrt((y)/(1-y))`
For x to be real `(y)/((1-y)) ge 0 " and " (1-y) ne 0`
`:.` range `(f) = {y in R : 0 le y lt 1}`
Also 1 and -1 have the same image `((1)/(2))`
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