Let f: R→R where f(x) = sinx . Show that f is into.

Q: Let f: R→R where f(x) = sinx . Show that f is into.

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Solution: Since co-domain of f is the set R whereas the range of f is the interval [-1, 1], hence f is into.

Can you make it onto?

The answer is ‘yes’, if you redefine the co-domain.

Let f be defined from R to another set Y = [-1, 1] i.e. f: R→Y where

f(x) = sinx, then f is onto as range f(x) = [-1, 1] = Y