The signum function, f: R → R is given by f(x) = begincases 1, textif x 0 0, textif x=0 -1, textif x

Question

The signum function, f: R → R is given by f(x) = begincases 1, textif x > 0 0, textif x=0 -1, textif x < 0 endcases is (A) One-one (B) Onto (C) Many-one (D) None of these

Tardigrade Admin · Accepted Answer

We have , f(1)= f(2)= f(3) = 1 f(0 ) = 0 f - (1) = f(-2) = f (-3) = - 1 Hence, function f is not one-one, so signum function is many-one function.

Q. The signum function, $f$ : $R \to R$ is given by
$f (x) = ⎩ ⎨ ⎧ 1, 0, - 1, if x > 0 if x = 0 if x < 0$ is

One-one

Onto

Many-one

None of these

We have , $f (1) = f (2) = f (3) = 1$
$f (0) = 0$
$f - (1) = f (- 2) = f (- 3) = - 1$
Hence, function $f$ is not one-one, so signum function is many-one function.

Q. The signum function, f : R→R is given by f(x)=⎩⎨⎧​1,0,−1,​if x>0if x=0if x<0​ is