Advertisements
Advertisements
प्रश्न

The given function f : R → R is not ‘onto’ function. Give reason.
Advertisements
उत्तर
Since each line in co-domain of the function parallel to x-axis, doesn’t cuts the graph of function at least one point, therefore the f(x) is not an onto function.
APPEARS IN
संबंधित प्रश्न
Check the injectivity and surjectivity of the following function:
f : N → N given by f(x) = x2
Let f: R → R be defined as f(x) = 10x + 7. Find the function g: R → R such that g o f = f o g = 1R.
Let A = {–1, 0, 1, 2}, B = {–4, –2, 0, 2} and f, g : A → B be functions defined by f(x) = x2 – x, x ∈ A and g(x) = `2|x - 1/2| – 1`, x ∈ A. Are f and g equal?
Justify your answer. (Hint: One may note that two functions f : A → B and g : A → B such that f(a) = g(a) ∀ a ∈ A are called equal functions.)
Let A = {−1, 0, 1} and f = {(x, x2) : x ∈ A}. Show that f : A → A is neither one-one nor onto.
Find gof and fog when f : R → R and g : R → R is defined by f(x) = x and g(x) = |x| .
Verify associativity for the following three mappings : f : N → Z0 (the set of non-zero integers), g : Z0 → Q and h : Q → R given by f(x) = 2x, g(x) = 1/x and h(x) = ex.
If f : A → B and g : B → C are one-one functions, show that gof is a one-one function.
Find fog and gof if : f (x) = ex g(x) = loge x .
Find fog and gof if : f (x) = x+1, g (x) = sin x .
Let A = R - {3} and B = R - {1}. Consider the function f : A → B defined by f(x) = `(x-2)/(x-3).`Show that f is one-one and onto and hence find f-1.
[CBSE 2012, 2014]
If A = {1, 2, 3, 4} and B = {a, b, c, d}, define any four bijections from A to B. Also give their inverse functions.
If f : R → R is defined by f(x) = 10 x − 7, then write f−1 (x).
Let A = {a, b, c, d} and f : A → A be given by f = {( a,b ),( b , d ),( c , a ) , ( d , c )} write `f^-1`. [NCERT EXEMPLAR]
Mark the correct alternative in the following question:
Let f : R→ R be defined as, f(x) = \[\begin{cases}2x, if x > 3 \\ x^2 , if 1 < x \leq 3 \\ 3x, if x \leq 1\end{cases}\]
Then, find f( \[-\]1) + f(2) + f(4)
Consider the set A containing n elements. Then, the total number of injective functions from A onto itself is ______
Let f: R → R be the function defined by f(x) = 2x – 3 ∀ x ∈ R. write f–1
Range of `"f"("x") = sqrt((1 - "cos x") sqrt ((1 - "cos x")sqrt ((1 - "cos x")....infty))`
Consider a set containing function A= {cos–1cosx, sin(sin–1x), sinx((sinx)2 – 1), etan{x}, `e^(|cosx| + |sinx|)`, sin(tan(cosx)), sin(tanx)}. B, C, D, are subsets of A, such that B contains periodic functions, C contains even functions, D contains odd functions then the value of n(B ∩ C) + n(B ∩ D) is ______ where {.} denotes the fractional part of functions)
Let A = {1, 2, 3, ..., 10} and f : A `rightarrow` A be defined as
f(k) = `{{:(k + 1, if k "is odd"),( k, if k "is even"):}`.
Then the number of possible functions g : A `rightarrow` A such that gof = f is ______.
If every seat in a classroom is occupied by one student, the situation resembles:
