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a
one-to-one and onto
b
one-to-one but not onto
c
onto but not one-to-one
d
neither one-to-one nor onto
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Correct option is A
Given that f(x)=2x+sinx,x∈R or f′(x)=2+cosx But −1≤cosx≤1 or 1≤2+cosx≤3∴ f′(x)>0∀x∈R Therefore, f(x) is strictly increasing and, hence, one-one. Also, as x→∞,f(x)→∞ , and x→−∞,f(x)→−∞ . Therefore, Hence, f(x) is onto. Thus, f(x) is one-one and onto.Similar Questions
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