Question

Check the injectivity and surjectivity of the Signum function.​

Answer 1

Answer:

injectivity denotes the one one nature of a function which is not so in the case of signum

because signum has value -1 for inputs less than 0, 0 for inputs equal to 0, and 1 for inputs greater than 0.

for example

my inputs are -4 and -2

then the value of their signum will be -1 .

therefore not injective

surjetctivity denotes the onto nature or the case in which codomain = range

Now, as f(x) takes only 3 values (1, 0, or - 1) for the element - 2 in co-domain R, there does not exist any x in domain R such that f(x) = - 2. ∴ f is not onto.

not surjective

Neither injective not surjective.