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Question

Let f:RR be defined as f(x)=3x. Choose the correct answer.
(a)f is one-one onto
(b)f is many -one onto
(c) f in one-one but not onto
(d) f is neither one-one nor onto

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Solution

f:RR is defined as f(x)=3x
Let x,yR such that f(x)=f(y).
3x=3yx=y
Therefore, f is one-one.
Also, for any real number (y)in co-domain R, there exists y3 in R such that f(y3)=3(y3)=y
Therefore, f is onto. Hence, function f is one-one and onto.
The correct answer is (a)


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