Home
Class 12
MATHS
If f: RvecR is given by f(x)=(x^2-4)/(x^...

If `f: RvecR` is given by `f(x)=(x^2-4)/(x^2+1)` , identify the type of function.

A

many-one & into

B

many-one & onto

C

one-one & into

D

one-one & onto

Text Solution

Verified by Experts

The correct Answer is:
A
`f(x)=f(-x), " So, "f` is many-one.
Also, `f(x)=1-(5)/(x^(2)+1) in [-4,1) " So, "f` is into.
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.5|5 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.6|8 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.3|9 Videos

  • Quadratic Equations, Inequalities, Modulus and Logarithms

    CENGAGE|Exercise Question Bank|31 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

If f:R rarr R is given by f(x)=(x^(2)-4)/(x^(2)+1) identify the type of function.

If f:R rarr is a function such that f(x)=x^(3)+x^(2)+3x+sin x, then identify the type of function.

The function f:R to R given by f(x)=x^(2)+x is

Let f(x) be a function given by f(x) =(x^2+1)/([x]) where [] denotes the greatest interger function .Then f(x) is monotonically

If the function f:R rarr A given by f(x)=(x^(2))/(x^(2)+1) is surjection,then find A

Let f(x) be a derivable function on RR such that its derivative function is given by f'(x) =(4x^2 - x^4-1)/(2(x^4+1)), then wrong statement is

Let f" [1,2] to (-oo,oo) be given by f(x)=(x^(4)+3x^(2)+1)/(x^(2)+1) then find value of in [f_(max)]" in "[-1,2] where [.] is greatest integer function :

Show that the function f given by f(x)=x^(3)-3x^(2)+4x,x in R

If f(x) is function such that f(x)=(z-1)^(2)(4-x), then