If A = [-1,1] then f: A arrow A defined by f(x) = sin π x is

Question

If A = [-1,1] then f: A arrow A defined by f(x) = sin π x is (A) one-one but not onto (B) onto but not one-one (C) neither one - one nor onto (D) bijective

Tardigrade Admin · Accepted Answer

f(0) = f(1) = 0 ⇒ f is not one-one Rang of f = [ - 1 , 1 ] = codomain ⇒ f is onto

Q. If $A = [- 1, 1]$ then $f : A \to A$ defined by $f (x) = sin π x$ is

one-one but not onto

onto but not one-one

neither one - one nor onto

bijective

f(0) = f(1) = 0 $\Rightarrow$ f is not one-one
Rang of f = [ - 1 , 1 ] = codomain $\Rightarrow$ f is onto

Q. If A=[−1,1] then f:A→A defined by f(x)=sinπx is