Advertisements
Advertisements
प्रश्न
Find gof and fog when f : R → R and g : R → R is defined by f(x) = 2x + x2 and g(x) = x3
Advertisements
उत्तर
Given, f : R → R and g : R → R
So, gof : R → R and fog : R → R
f(x) = 2x + x2 and g(x) = x3
(gof) (x)
= g (f (x))
= g (2x+x2)
= (2x+x2)3
(fog) (x)
= f (g (x))
= f (x3)
= 2 (x3)+(x3)2
=2x3+x6
APPEARS IN
संबंधित प्रश्न
Show that the function f in `A=R-{2/3} ` defined as `f(x)=(4x+3)/(6x-4)` is one-one and onto hence find f-1
Check the injectivity and surjectivity of the following function:
f : N → N given by f(x) = x3
Check the injectivity and surjectivity of the following function:
f : Z → Z given by f(x) = x3
In the following case, state whether the function is one-one, onto or bijective. Justify your answer.
f : R → R defined by f(x) = 3 – 4x
Let A and B be sets. Show that f : A × B → B × A such that f(a, b) = (b, a) is bijective function.
Classify the following function as injection, surjection or bijection : f : Z → Z given by f(x) = x2
Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of each of the following:
(i) an injective map from A to B
(ii) a mapping from A to B which is not injective
(iii) a mapping from A to B.
Find gof and fog when f : R → R and g : R → R is defined by f(x) = x2 + 8 and g(x) = 3x3 + 1 .
Consider f : N → N, g : N → N and h : N → R defined as f(x) = 2x, g(y) = 3y + 4 and h(z) = sin z for all x, y, z ∈ N. Show that ho (gof) = (hog) of.
Give examples of two functions f : N → Z and g : Z → Z, such that gof is injective but gis not injective.
Find fog and gof if : f (x) = |x|, g (x) = sin x .
Find f −1 if it exists : f : A → B, where A = {1, 3, 5, 7, 9}; B = {0, 1, 9, 25, 49, 81} and f(x) = x2
Let f be a function from R to R, such that f(x) = cos (x + 2). Is f invertible? Justify your answer.
If f : R → R is defined by f(x) = x2, write f−1 (25)
If f : C → C is defined by f(x) = x4, write f−1 (1).
Let f be an invertible real function. Write ( f-1 of ) (1) + ( f-1 of ) (2) +..... +( f-1 of ) (100 )
Write the domain of the real function
`f (x) = sqrt([x] - x) .`
Let f : R → R be the function defined by f(x) = 4x − 3 for all x ∈ R Then write f . [NCERT EXEMPLAR]
The function
\[f : R \to R\] defined by\[f\left( x \right) = \left( x - 1 \right) \left( x - 2 \right) \left( x - 3 \right)\]
(a) one-one but not onto
(b) onto but not one-one
(c) both one and onto
(d) neither one-one nor onto
Let
Mark the correct alternative in the following question:
If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is
If f(x) = `(x+3)/(4x−5) , "g"(x) = (3+5x)/(4x−1)` then verify that `("fog") (x)` = x.
For sets A, B and C, let f: A → B, g: B → C be functions such that g o f is surjective. Then g is surjective.
Let the function f: R → R be defined by f(x) = cosx, ∀ x ∈ R. Show that f is neither one-one nor onto
Let X = {1, 2, 3}and Y = {4, 5}. Find whether the following subset of X ×Y are function from X to Y or not
h = {(1,4), (2, 5), (3, 5)}
Let X = {1, 2, 3}and Y = {4, 5}. Find whether the following subset of X ×Y are function from X to Y or not
k = {(1,4), (2, 5)}
Let A = [–1, 1]. Then, discuss whether the following functions defined on A are one-one, onto or bijective:
g(x) = |x|
Let A = [–1, 1]. Then, discuss whether the following functions defined on A are one-one, onto or bijective:
h(x) = x|x|
Let f: `[2, oo)` → R be the function defined by f(x) = x2 – 4x + 5, then the range of f is ______.
If N be the set of all-natural numbers, consider f: N → N such that f(x) = 2x, ∀ x ∈ N, then f is ____________.
Raji visited the Exhibition along with her family. The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by y = x2.
Answer the following questions using the above information.
- Let f: {1,2,3,....} → {1,4,9,....} be defined by f(x) = x2 is ____________.
Raji visited the Exhibition along with her family. The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by y = x2.
Answer the following questions using the above information.
- The function f: Z → Z defined by f(x) = x2 is ____________.
Let the function f: R → R be defined by f(x) = 4x – 1, ∀ x ∈ R then 'f' is
Difference between the greatest and least value of f(x) = `(1 + (cos^-1x)/π)^2 - (1 + (sin^-1x)/π)^2` is ______.
Let x is a real number such that are functions involved are well defined then the value of `lim_(t→0)[max{(sin^-1 x/3 + cos^-1 x/3)^2, min(x^2 + 4x + 7)}]((sin^-1t)/t)` where [.] is greatest integer function and all other brackets are usual brackets.
