JEE MATHEMATICS MCQ: FUNCTIONS

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Analyzing +4 | -1

Let

f(x)=p x^2+q x+r ; p, q, r \in R

and if

f(x)-x=0

has no real roots then

f(f(x))-x=0

has

View answer and explanation

Correct option: C

No real root

Option C (No real root) is correct because if f(x) - x = 0 has no real roots, then f(x) is always greater or always less than x, implying f(f(x)) - x = 0 also has no real roots.

More Questions from FUNCTIONS

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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