Advertisements
Advertisements
प्रश्न
Let f : R → R, g : R → R be two functions defined by f(x) = x2 + x + 1 and g(x) = 1 − x2. Write fog (−2).
उत्तर
\[\left( fog \right)\left( - 2 \right) = f \left( g \left( - 2 \right) \right)\]
\[ = f\left( 1 - \left( - 2 \right)^2 \right)\]
\[ = f\left( - 3 \right)\]
\[ = \left( - 3 \right)^2 + \left( - 3 \right) + 1\]
\[ = 9 - 3 + 1\]
\[ = 7\]
APPEARS IN
संबंधित प्रश्न
Show that the function f: R* → R* defined by `f(x) = 1/x` is one-one and onto, where R* is the set of all non-zero real numbers. Is the result true if the domain R* is replaced by N, with co-domain being same as R?
Following the case, state whether the function is one-one, onto, or bijective. Justify your answer.
f: R → R defined by f(x) = 1 + x2
Let A = {−1, 0, 1} and f = {(x, x2) : x ∈ A}. Show that f : A → A is neither one-one nor onto.
Let A = [-1, 1]. Then, discuss whether the following function from A to itself is one-one, onto or bijective : g(x) = |x|
Let A = [-1, 1]. Then, discuss whether the following functions from A to itself is one-one, onto or bijective : h(x) = x2
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+1, g(x) = `e^x`
.
Find fog and gof if : f(x) = sin−1 x, g(x) = x2
If f, g : R → R be two functions defined as f(x) = |x| + x and g(x) = |x|- x, ∀x∈R" .Then find fog and gof. Hence find fog(–3), fog(5) and gof (–2).
Find f −1 if it exists : f : A → B, where A = {0, −1, −3, 2}; B = {−9, −3, 0, 6} and f(x) = 3 x.
Let A and B be two sets, each with a finite number of elements. Assume that there is an injective map from A to B and that there is an injective map from B to A. Prove that there is a bijection from A to B.
If f : A → A, g : A → A are two bijections, then prove that fog is a surjection ?
If f : C → C is defined by f(x) = x4, write f−1 (1).
Let \[f : \left( - \frac{\pi}{2}, \frac{\pi}{2} \right) \to R\] be a function defined by f(x) = cos [x]. Write range (f).
Let f : R → R+ be defined by f(x) = ax, a > 0 and a ≠ 1. Write f−1 (x).
Let f : R − {−1} → R − {1} be given by\[f\left( x \right) = \frac{x}{x + 1} . \text{Write } f^{- 1} \left( x \right)\]
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) = sqrtx - [x] .`
Write the domain of the real function
`f (x) = sqrt([x] - x) .`
If f(x) = x + 7 and g(x) = x − 7, x ∈ R, write fog (7).
What is the range of the function
`f (x) = ([x - 1])/(x -1) ?`
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. State whether f is one-one or not.
Let f, g : R → R be defined by f(x) = 2x + l and g(x) = x2−2 for all x
∈ R, respectively. Then, find gof. [NCERT EXEMPLAR]
\[f : Z \to Z\] be given by
` f (x) = {(x/2, ", if x is even" ) ,(0 , ", if x is odd "):}`
Then, f is
If the function
\[f : R \to R\] be such that
\[f\left( x \right) = x - \left[ x \right]\] where [x] denotes the greatest integer less than or equal to x, then \[f^{- 1} \left( x \right)\]
If \[g\left( x \right) = x^2 + x - 2\text{ and} \frac{1}{2} gof\left( x \right) = 2 x^2 - 5x + 2\] is equal to
Write about strcmp() function.
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
The function f : R → R given by f(x) = x3 – 1 is ____________.
Let f : [0, ∞) → [0, 2] be defined by `"f" ("x") = (2"x")/(1 + "x"),` then f is ____________.
A function f: x → y is said to be one – one (or injective) if:
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.
Let f(n) = `[1/3 + (3n)/100]n`, where [n] denotes the greatest integer less than or equal to n. Then `sum_(n = 1)^56f(n)` is equal to ______.
The given function f : R → R is not ‘onto’ function. Give reason.
