Home
Class 12
MATHS
If f(x)=int(x^8+4)/(x^4-2x^2+2)dxa n df(...

If `f(x)=int(x^8+4)/(x^4-2x^2+2)dxa n df(0)=0,t h e n` `f(x)` is an odd function `f(x)` has range `R` `f(x)` has at least one real root `f(x)` is a monotonic function.

A

f(x) is an odd functtion

B

f(x) has range R

C

f(x) has at least one real root

D

f(x) is monotonic function

Text Solution

Verified by Experts

The correct Answer is:
A, B
Promotional Banner

Topper's Solved these Questions

  • IDENFINITE INTEGRAL

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Integar Answer Type)|5 Videos
  • IDENFINITE INTEGRAL

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination ( Matrix Match Type)|2 Videos
  • IDENFINITE INTEGRAL

    CHHAYA PUBLICATION|Exercise Long Answer Type Questions|15 Videos
  • GENERAL SOLUTIONS OF TRIGNOMETRIC EQUATIONS

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type-|2 Videos
  • INCREASING AND DECREASING FUNCTION

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

Similar Questions

Explore conceptually related problems

If f(x)=int(x^8+4)/(x^4-2x^2+2)dx and f(0)=0,t h e n (a) f(x) is an odd function (b) f(x) has range R (c) f(x) has at least one real root (d) f(x) is a monotonic function.

If f(x+y)+f(x-y)=2f(x).f(y) AA x,y in R . f(0)ne0 , find if f(x) is even or odd function.

If f'(x)=(1-2sin^2x)/f(x), (f(x) ge 0, AA x in R and f(0)=1) then f(x) is a periodic function with the period

If int(x^2-x+1)/((x^2+1)^(3/2))e^x dx=e^xf(x)+c , then (a) f(x) is an even function (b) f(x) is a bounded function (c) the range of f(x) is (0,1) (d) f(x) has two points of extrema

If f(x)=|x-2| a n d g(x)=f[f(x)],t h e n g^(prime)(x)= ______ for x>20

Let f:(-pi/2,pi/2)vecR be given by f(x)=(log(sec"x"+tan"x"))^3 then f(x) is an odd function f(x) is a one-one function f(x) is an onto function f(x) is an even function

Ifint(x^4+1)/(x^6+1)dx=tan^(-1)f(x)-2/3tan^(-1)g(x)+C ,t h e n a) both f(x)a n dg(x) are odd functions b) f(x) is monotonic function c) f(x)=g(x) has no real roots d) int(f(x))/(g(x))dx=-1/x+3/(x^3)+c

f(x) satisfies the relation f(x)-lamda int_(0)^(pi//2)sinxcostf(t)dt=sinx If f(x)=2 has the least one real root, then

If f(t) is an odd function, then int_(0)^(x)f(t) dt is -