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JEE MATHEMATICS MCQ: FUNCTIONS

1 Easy

1 of 1

Analyzing +4 | -1

Let

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

. Then the set

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

contains

View answer and explanation

Correct option: C

\{0,-1\}

The correct answer is C ({0,-1}) because the set

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

contains 0 and -1, found by solving

f(f(x)) = x

for

x \geq -1

.

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

f(x)=x(4-x)

f^{-1}(x)

is given by: If

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

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

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

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

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

f: R \rightarrow R

f(x)=x^4

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

f(x + y) = f(x)f(y)

\sum\limits_{x = 1}^\infty {f(x) = 2,x,y \in N},

where N is the set of all natural numbers, then the value of

\frac{{f(4)}}{{f(2)}}