New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Functions question

2021 · 24 Feb · Shift 1 · Q26

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Functions
2021 · 24 Feb · Shift 1 · Q26

Functions question

2021 · 24 Feb · Shift 1 · Q26

JEE MainMathematicsFunctionsMCQ+4 / −1

Let f : R → R be defined as f (x) = 2x – 1 and g : R - {1} → R be defined as g(x) =

{{x - {1 \over 2}} \over {x - 1}}

. Then the composition function f(g(x)) is :

A
one-one but not onto
B
onto but not one-one
C
both one-one and onto
D
neither one-one nor onto

More from Functions

If a + $α$ = 1, b + $β$ = 2 and $a f (x) + α f (\frac{1}{x}) = b x + \frac{β}{x}, x e 0$ , then the value of the expression $\frac{f ( x ) + f ( \frac{1}{x} )}{x + \frac{1}{x}}$ is …2021 · Numerical
Let f, g : N $\to$ N such that f(n + 1) = f(n) + f(1) $\forall$ n $\in$ N and g be any arbitrary function. Which of the following statements is NOT true?2021 · MCQ
A function f(x) is given by $f (x) = \frac{5 ^{x}}{5 ^{x} + 5}$ , then the sum of the series $f (\frac{1}{20}) + f (\frac{2}{20}) + f (\frac{3}{20}) + ....... + f (\frac{39}{20})$ …2021 · MCQ
Let x denote the total number of one-one functions from a set A with 3 elements to a set B with 5 elements and y denote the total number of one-one functions form the set A to the set A $\times$ B. Then :2021 · MCQ
Let g : N $\to$ N be defined as g(3n + 1) = 3n + 2, g(3n + 2) = 3n + 3, g(3n + 3) = 3n + 1, for all n $\geq$ 0. Then which of the following statements is true?2021 · MCQ
Consider function f : A $\to$ B and g : B $\to$ C (A, B, C $\subseteq$ R) such that (gof) $-$ 1 exists, then :2021 · MCQ
Let $A = {1, 2, 3, ...., 10}$ and $f : A \to A$ be defined as $f (k) = {k + 1 k i f k i s o dd i f k i s e v e n$ Then the number of possible functions $g : A \to A$ such that…2021 · MCQ
Let S = {1, 2, 3, 4, 5, 6, 7}. Then the number of possible functions f : S $\to$ S such that f(m . n) = f(m) . f(n) for every m, n $\in$ S and m . n $\in$ S is equal to .2021 · Numerical