Advertisements
Advertisements
Question
Let f: R → R be given by f(x) = tan x. Then f–1(1) is ______.
Options
`pi/4`
`{"n" pi + pi/4 : "n" ∈ "Z"}`
Does not exist
None of these
Advertisements
Solution
Let f: R → R be given by f(x) = tan x. Then f–1(1) is `pi/4`.
Explanation:
Given that, f(x) = tan x
Let y = tan x
⇒ x = tan–1y
⇒ f–1(x) = tan–1x
⇒ f–1(1) = tan–11 = `pi/4`
APPEARS IN
RELATED QUESTIONS
Check the injectivity and surjectivity of the following function:
f : R → R given by f(x) = x2
Show that the signum function f : R → R, given by
`f(x) = {(1", if" x > 0), (0", if" x = 0), (-1", if" x < 0):}`
is neither one-one nor onto.
Classify the following function as injection, surjection or bijection :
f : R → R, defined by f(x) = 1 + x2
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 surjective functions f1 and f2 from Z to Z such that f1 + f2 is not surjective.
Let f : R → R and g : R → R be defined by f(x) = x2 and g(x) = x + 1. Show that fog ≠ gof.
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.
Let f(x) = x2 + x + 1 and g(x) = sin x. Show that fog ≠ gof.
If f(x) = sin x and g(x) = 2x be two real functions, then describe gof and fog. Are these equal functions?
If f : Q → Q, g : Q → Q are two functions defined by f(x) = 2 x and g(x) = x + 2, show that f and g are bijective maps. Verify that (gof)−1 = f−1 og −1.
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).
If f : R → R is defined by f(x) = 10 x − 7, then write f−1 (x).
Let A = {1, 2, 3, 4} and B = {a, b} be two sets. Write the total number of onto functions from A to B.
Write the domain of the real function
`f (x) = sqrtx - [x] .`
If f : R → R be defined by f(x) = (3 − x3)1/3, then find fof (x).
Let M be the set of all 2 × 2 matrices with entries from the set R of real numbers. Then, the function f : M→ R defined by f(A) = |A| for every A ∈ M, is
The range of the function
\[f\left( x \right) =^{7 - x} P_{x - 3}\]
Let \[f\left( x \right) = x^2 and g\left( x \right) = 2^x\] Then, the solution set of the equation
If \[f\left( x \right) = \sin^2 x\] and the composite function \[g\left( f\left( x \right) \right) = \left| \sin x \right|\] then g(x) is equal to
Let \[f\left(x\right) = x^3\] be a function with domain {0, 1, 2, 3}. Then domain of \[f^{-1}\] is ______.
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)
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
The domain of the function f: R → R defined by f(x) = `sqrt(x^2 - 3x + 2)` is ______
Let A be a finite set. Then, each injective function from A into itself is not surjective.
Let D be the domain of the real valued function f defined by f(x) = `sqrt(25 - x^2)`. Then, write D
Let the function f: R → R be defined by f(x) = cosx, ∀ x ∈ R. Show that f is neither one-one nor onto
If f(x) = (4 – (x – 7)3}, then f–1(x) = ______.
Let A = {0, 1} and N be the set of natural numbers. Then the mapping f: N → A defined by f(2n – 1) = 0, f(2n) = 1, ∀ n ∈ N, is onto.
Let R be a relation on the set L of lines defined by l1 R l2 if l1 is perpendicular to l2, then relation R is ____________.
A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever
Let I be the set of all citizens of India who were eligible to exercise their voting right in the general election held in 2019. A relation ‘R’ is defined on I as follows:
R = {(V1, V2) ∶ V1, V2 ∈ I and both use their voting right in the general election - 2019}
- Mr. ’X’ and his wife ‘W’ both exercised their voting right in the general election-2019, Which of the following is true?
An organization conducted a bike race under 2 different categories-boys and girls. Totally there were 250 participants. Among all of them finally, three from Category 1 and two from Category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project. Let B = {b1,b2,b3} G={g1,g2} where B represents the set of boys selected and G the set of girls who were selected for the final race.
Ravi decides to explore these sets for various types of relations and functions.
- Ravi wants to know among those relations, how many functions can be formed from B to G?
Let f: R → R defined by f(x) = x4. Choose the correct answer
Let f: R → R defined by f(x) = 3x. Choose the correct answer
The domain of function is f(x) = `sqrt(-log_0.3(x - 1))/sqrt(x^2 + 2x + 8)` is ______.
Let S = {1, 2, 3, 4, 5, 6, 7}. Then the number of possible functions f: S `rightarrow` S such that f(m.n) = f(m).f(n) for every m, n ∈ S and m.n ∈ S is equal to ______.
Which one of the following graphs is a function of x?
 |
 |
| Graph A | Graph B |
The trigonometric equation tan–1x = 3tan–1 a has solution for ______.
