Let the function f: R → R be defined by f (x) = cos x, ∀ x ∈ R. Show that f is neither one-one nor onto.

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Harshit Singh · Answer

Dear Student We have, f: R &rarr; R, f(x) = cos x Now, f (x1) = f (x2) cos x1= cos x2 x1=2n&pi;&plusmn;x2,n&isin;Z It&rsquo;s seen that the above equation has infinite solutions for x1and x2Hence, f(x) is many one function. Also the range of cos x is [-1, 1], which is subset of given co-domain R. Thus,the given function is not onto. Thanks

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Let the function f: R → R be defined by f (x) = cos x, ∀ x ∈ R. Show that f is neither one-one nor onto.

Let the function f: R → R be defined by f (x) = cos x, ∀ x ∈ R. Show that f is neither one-one nor onto.

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Let the function f: R → R be defined by f (x) = cos x, ∀ x ∈ R. Show that f is neither one-one nor onto.

Let the function f: R → R be defined by f (x) = cos x, ∀ x ∈ R. Show that f is neither one-one nor onto.

1 Answers

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