JEE MATHEMATICS MCQ: FUNCTIONS

1 Hard

1 of 1

Understanding +4 | -1

Let

f:R \to R

be a function defined by

f\left( x \right) = - \frac{{{{\left| x \right|}^3} + \left| x \right|}}{{1 + {x^2}}},

then the graph of

f\left( x \right)

lies in the

View answer and explanation

Correct option: D

III and IV quadrants

Option D (III and IV quadrants) is correct because the function

f(x)

is always negative or zero, causing its graph to lie in the third and fourth quadrants.

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

f(x)=x(4-x)

f^{-1}(x)

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

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

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