alleryFor f(x) = 2x from R to R, the function is:
AOnly one-one, not onto
BOnly onto, not one-one
CNeither one-one nor onto
DBoth one-one and onto
Answer & Solution
Correct answer: D. Both one-one and onto
1. Doubling distinct reals gives distinct reals, so f is one-one.
2. Any real y is reached by taking x as half of y.
3. So over the reals the same rule is one-one and onto.
_Source: syllabus Mathematics Part I, Chapter 1, Relations and Functions._
Keep practising Relations and Functions
Browse all Relations and Functions questions for CBSE Class 12 (Commerce), or explore more Mathematics topics.
Related questions
In N, R = {(x, y): y = x + 5 and x < 4} isOn {0,...,12}, with R = {(a, b): a = b}, the set of elements related to 1 isHow many different relations can be defined on a 3 element set?A relation from A to B is defined as an arbitrary subset ofOn subsets of X, 'A is a subset of B' fails to be an equivalence because it is notOn [0, pi/2], f = sin x and g = cos x. f + g takes the value 1 atWhy is x to 2x (that is, I_N + I_N) from N to N not onto?How many one-one functions map {1, 2, 3} onto itself?