Let `f : R -> R` be a continuous onto function satisfying `f(x) + f(-x)=0 AA x in R`,. If `f(-3) = 2` and `f(5) = 4` in `[-5, 5]` , then the equation `f(x) = 0` has

Options

A. exactly 2 real roots.
B. exactly 3 real roots.
C. atleast 3 real roots.
D. atleast 5 real roots.

Answer

A

Explanation

`"Given "f(x)=-f(-x)" in "[-5,5]`
`rArr" "f(x)` is an odd function.
Since points (-3,2), (-1,-3) and (5,4) lies on the curve.
So, (3,-2), (1,3) and (-5,-4) will also lies on the curve.
For minimun number of roots, one of the possible graph of continuous function f(x) is as follows.

`rArr" "f(x)=0` has atleast 5 solutions.