JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1

Let

{g}: {R} \rightarrow {R}

be given by

g(x)=3+4 {x}

. If

g^{{n}}({x})=\underbrace{{ gogo } \ldots \ldots \ldots og({x})}_{n \, {\text {times }}}

then

g^{-{n}}({x})=

(where

g^{-n}(x)

denotes inverse of

g^{{n}}({x})

)

View answer and explanation

Correct option: B

(x+1) 4^{-n}-1

Option B (

(x+1) 4^{-n}-1

) is the correct answer because it represents the inverse of the nth composition of the function g(x), derived by finding the inverse function and composing it n times.

More Questions from FUNCTIONS

Practice All Chapter MCQs →

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