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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.
Dear StudentWe have,f: R → R, f(x) = cos xNow,f (x1) = f (x2)cos x1= cos x2x1=2nπ±x2,n∈ZIt’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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