First slide

Functions (XII)

Question

Let f : R → R be a function defined by $f (x) = - (\frac{| x |^{3} + | x |}{1 + x^{2}})$ , then the graph of f (x) lies in which quadrant

Moderate

A

I
B

II
C

III
D

IV

Solution

Since, f (– x) = f (x)
⇒ f (x) is an even function, its graph will be symmetrical about y-axis.
$Also, f (x) = - (\frac{| x |^{3} + | x |}{1 + x^{2}})$
⇒ f (x) = –(positive) = negative
i.e., the graph of f (x) completely lies below the x-axis, and
is also symmetric about y-axis (as discussed above).
$∴$ The graph of f (x) lies in III and IV quadrants.
The correct option is (3)and (4)

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