Question

Which of the following functions is NOT injective?

• A. $f(x) = x^3 + 4$ from R to R
• B. $f(x) = x^3 + 4$ from N to N
• C. $f(x) = x^2 + 4$ from R to R
• D. $f(x) = x^2 + 4$ from N to N

Answer 1

I think C) since it is many to one

That is it is giving same value on positive and negative value of x.

for example, On +2 it is giving 8 and on -2 also it is giving 8. So it is many to one and hence not injective

Answer 2

c) f(x) = x² + 4 from R to R is not injective

See injective means one to one function

N here is natural number . Range of Natural number is 0 to +infinity

So, natural number has no chances to be many to one or one to many or many to many relationship.

R is real number. Range of Real number -infinity to +infinity.

So, it has a chance of giving same output in positive and negative numbers

Say, for x= -1,1 f(x) = x^2 + 4 from R to R gets same value.

So, C will be answer