Question

How many of the following are functions ?

(i) f(x) = $x^5;\{-1,0,1\}\to \{0,1,2\}$

(ii) f(x) = $\pm \sqrt{x};\{0,4,9\}\to \{0,2,-2,3,-3\}$

(iii) f(x) = $\sqrt{x};\{0,4,9\}\to \{0,2,-2,3,-3\}$

(iv) f(x) = $x^2;\{0,1,2\}\to \{0,1,2,3,4\}$

• A. (i)
• B. (ii)&(iii)
• C. (iii)
• D. (iii) & (iv)

Answer 1

The correct option is D

(iii) & (iv)

(i) f (-1) = -1, but co-domain doesn't contain -1. Therefore it is not a function
(ii) f(4) = ±2, In a function, an element from the domain can be mapped to only one element in the co-domain. (ii) is not a function as 4 is mapped to both 2 and -2.
(iii) and (iv) are functions as they satisfy the definition of function.(i.e, each element in the first set has one and only one image)