Question

How many of the following are functions ?

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

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

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

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

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

Answer 1

The correct option is D

(iii) & (iv)

(i) f (-1) = -1, but there is no -1 in the second set. So its not a function
(ii) f(4) = $\pm$ 2, in a function, an element will be mapped to only one element. So, (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)