JEE MATHEMATICS MCQ: FUNCTIONS

1 Easy

1 of 1

Analyzing +4 | -1

Let

f:\{x, y, z\} \rightarrow\{1,2,3\}

be a one-one function. If it is given that exactly one of the following statements is true,

Statement-1:

f(x)=1

, Statement-2:

f(y) \neq 1

, Statement-3:

f(z) \neq 2

.

then

f^{-1}

(1) is

View answer and explanation

Correct option: B

y

Option B (y) is correct because if f(x) = 1, then f(y) cannot be 1, violating the one-one property. If f(z) = 1, statements 2 and 3 are both true, which is not allowed. Therefore, f(y) = 1.

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f:(-\infty, 2] \longrightarrow(-\infty, 4]

, where

f(x)=x(4-x)

, then

f^{-1}(x)

is given by: If

g(f(x))=|\sin x|

and

f(g(x))=(\sin \sqrt{x})^2

, then Let

f:\left( {2,\;3} \right) \to \left( {0,\;1} \right)

be defined by

f\left( x \right) = x - \left[ x \right]

, then

{f^{ - 1}}\left( x \right)

equals Let

f: R \rightarrow R

be defined as

f(x)=x^4

, Choose the correct answer. Which of the following functions are odd functions Let

f(x)=(x+1)^2-1(x \geq-1)

. Then the set

S=\left\{x: f(x)=f^{-1}(x)\right\}

contains