Home
Class 12
MATHS
Let f : R to R be a continuous onto f...

Let ` f : R to R ` be a continuous onto function satisfying `f(x)+f(-x) = 0, forall x in R` . If `f(-3) = 2 and f(5) = 4 ` in [-5, 5], then what is the minimum number of roots of the equation f(x) = 0?

Text Solution

Verified by Experts

` f(x)+ f(-x) = 0`
f(x) is an odd function.
Since the points (-3, 2) and (5, 4) lie on the curve, (3, -2) and (-5, -4) will also lie on the curve.
For minimum number of roots, graph of the continuous function f(x) is as follows.

From the above graph of f(x), it is clear that equation f (x) = 0 has at least three real roots.
Promotional Banner

Topper's Solved these Questions

  • GETTING STARTED WITH GRAPHS

    CENGAGE ENGLISH|Exercise ILLUSTRATION 1.12|1 Videos

  • GETTING STARTED WITH GRAPHS

    CENGAGE ENGLISH|Exercise ILLUSTRATION 1.13|1 Videos

  • GETTING STARTED WITH GRAPHS

    CENGAGE ENGLISH|Exercise ILLUSTRATION 1.10|1 Videos

  • FUNCTIONS

    CENGAGE ENGLISH|Exercise Comprehension Type|7 Videos

  • GRAPH OF INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise Exercises|18 Videos

Similar Questions

Explore conceptually related problems

Let f: R->R be a continuous onto function satisfying f(x)+f(-x)=0AAx in R . If f(-3)=2 \ a n d \ f(5)=4 \ i n \ [-5,5], then the minimum number of roots of the equation f(x)=0 is

Let f(x) be a function satisfying f(x) + f(x+2) = 10 AA x in R , then

Let f:R to R be a function satisfying f(x+y)=f(x)=lambdaxy+3x^(2)y^(2)"for all "x,y in R If f(3)=4 and f(5)=52, then f'(x) is equal to

Let f be the continuous and differentiable function such that f(x)=f(2-x), forall x in R and g(x)=f(1+x), then

A function f : R -> R^+ satisfies f(x+y)= f(x) f(y) AA x in R If f'(0)=2 then f'(x)=

Let f be a differentiable function satisfying f '(x) =2 f(x) +10 AA x in R and f (0) =0, then the number of real roots of the equation f (x)+ 5 sec ^(2) x=0 ln (0, 2pi) is:

Let f:R rarr R be a continuous function such that f(x)-2f(x/2)+f(x/4)=x^(2) . f(3) is equal to

Let f: R to R be a continuous function which satisfies f(x)= int_0^xf(t)dtdot Then the value of f(1n5) is______

Let f:R rarr R be a continuous function such that f(x)-2f(x/2)+f(x/4)=x^(2) . f'(0) is equal to

Let f(x) be a continuous function such that f(0) = 1 and f(x)=f(x/7)=x/7 AA x in R, then f(42) is