Advertisements
Advertisements
प्रश्न
Find gof and fog when f : R → R and g : R → R is defined by f(x) = 2x + 3 and g(x) = x2 + 5 .
Advertisements
उत्तर
Given, f : R → R and g : R → R
So, gof : R → R and fog : R → R
f(x) = 2x + 3 and g(x) = x2 + 5
Now, (gof) (x)
= g (f (x))
= g (2x +3)
= (2x + 3)2 + 5
= 4x2+ 9 + 12x +5
=4x2+ 12x + 14
(fog) (x)
=f (g (x))
= f (x2 + 5)
= 2 (x2 + 5) +3
= 2 x2+ 10 + 3
= 2x2 + 13
APPEARS IN
संबंधित प्रश्न
Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Show that f is one-one.
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 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.
Show that the function f : R → R given by f(x) = x3 is injective.
Which of the following functions from A to B are one-one and onto?
f2 = {(2, a), (3, b), (4, c)} ; A = {2, 3, 4}, B = {a, b, c}
Let A = {−1, 0, 1} and f = {(x, x2) : x ∈ A}. Show that f : A → A is neither one-one nor onto.
Set of ordered pair of a function? If so, examine whether the mapping is injective or surjective :{(x, y) : x is a person, y is the mother of x}
If A = {1, 2, 3}, show that a one-one function f : A → A must be onto.
Give examples of two surjective functions f1 and f2 from Z to Z such that f1 + f2 is not surjective.
Find gof and fog when f : R → R and g : R → R is defined by f(x) = 2x + x2 and g(x) = x3
If f(x) = |x|, prove that fof = f.
Let f be a real function given by f (x)=`sqrt (x-2)`
Find each of the following:
(i) fof
(ii) fofof
(iii) (fofof) (38)
(iv) f2
Also, show that fof ≠ `f^2` .
State with reason whether the following functions have inverse :
f : {1, 2, 3, 4} → {10} with f = {(1, 10), (2, 10), (3, 10), (4, 10)}
State with reason whether the following functions have inverse :
g : {5, 6, 7, 8} → {1, 2, 3, 4} with g = {(5, 4), (6, 3), (7, 4), (8, 2)}
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 : [−1, ∞) → [−1, ∞) be given by f(x) = (x + 1)2 − 1, x ≥ −1. Show that f is invertible. Also, find the set S = {x : f(x) = f−1 (x)}.
Let A = {x &epsis; R | −1 ≤ x ≤ 1} and let f : A → A, g : A → A be two functions defined by f(x) = x2 and g(x) = sin (π x/2). Show that g−1 exists but f−1 does not exist. Also, find g−1.
If A = {1, 2, 3} and B = {a, b}, write the total number of functions from A to B.
If A = {a, b, c} and B = {−2, −1, 0, 1, 2}, write the total number of one-one functions from A to B.
If f : C → C is defined by f(x) = x2, write f−1 (−4). Here, C denotes the set of all complex numbers.
Let `f : R - {- 3/5}` → R be a function defined as `f (x) = (2x)/(5x +3).`
f-1 : Range of f → `R -{-3/5}`.
Which one the following relations on A = {1, 2, 3} is a function?
f = {(1, 3), (2, 3), (3, 2)}, g = {(1, 2), (1, 3), (3, 1)} [NCERT EXEMPLAR]
The function \[f : [0, \infty ) \to \text {R given by } f\left( x \right) = \frac{x}{x + 1} is\]
The function f : [-1/2, 1/2, 1/2] → [-π /2,π/2], defined by f (x) = `sin^-1` (3x - `4x^3`), is
Let
\[f : R \to R\] be a function defined by
For sets A, B and C, let f: A → B, g: B → C be functions such that g o f is injective. Then both f and g are injective functions.
Let the function f: R → R be defined by f(x) = cosx, ∀ x ∈ R. Show that f is neither one-one nor onto
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|
Using the definition, prove that the function f: A→ B is invertible if and only if f is both one-one and onto
Which of the following functions from Z into Z are bijections?
Let f : R → R be defind by f(x) = `1/"x" AA "x" in "R".` Then f is ____________.
Let f : [0, ∞) → [0, 2] be defined by `"f" ("x") = (2"x")/(1 + "x"),` 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 : N → R be defined by f(x) = x2. Range of the function among the following is ____________.
If log102 = 0.3010.log103 = 0.4771 then the number of ciphers after decimal before a significant figure comes in `(5/3)^-100` is ______.
A function f : [– 4, 4] `rightarrow` [0, 4] is given by f(x) = `sqrt(16 - x^2)`. Show that f is an onto function but not a one-one function. Further, find all possible values of 'a' for which f(a) = `sqrt(7)`.
The given function f : R → R is not ‘onto’ function. Give reason.
