Home
Class 12
MATHS
f: R->R is defined by f(x)=(e^x^2-e^-x^2...

`f: R->R` is defined by `f(x)=(e^x^2-e^-x^2)/(e^x^2+e^-x^2)` is (a) one-one but not onto (b) many-one but onto (c) one-one and onto (d) neither one-one nor onto

Text Solution

AI Generated Solution

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA ENGLISH|Exercise All Questions|90 Videos

  • HIGHER ORDER DERIVATIVES

    RD SHARMA ENGLISH|Exercise All Questions|179 Videos

Similar Questions

Explore conceptually related problems

If a function f:[2,\ oo)->R defined by f(x)=(x-1)(x-2)(x-3) is (a) one-one but not onto (b) onto but not one-one (c) both one and onto (d) neither one-one nor onto

Let f: R->R be a function defined by f(x)=(x^2-8)/(x^2+2) . Then, f is (a) one-one but not onto (b) one-one and onto (c) onto but not one-one (d) neither one-one nor onto

The function f:R rarr R defined as f(x)=(3x^2+3x-4)/(3+3x-4x^2) is : (a) One to one but not onto (b) Onto but not one to one (c) Both one to one and onto (d)Neither one to one nor onto

The function f: R->R defined by f(x)=2^x+2^(|x|) is (a) one-one and onto (b) many-one and onto (c) one-one and into (d) many-one and into

The function f:[0,3]->[1,29] , defined by f(x)=2x^3−15x^2+36x+1 , is (a) one-one and onto (b) onto but not one-one (c) one-one but not onto (d) neither one-one nor onto

The function f: R->R defined by f(x)=6^x+6^(|x|) is (a) one-one and onto (b) many one and onto (c) one-one and into (d) many one and into

The function f : R rarr [ -1,1 ] defined by f(x) = cos x is (a) both one-one and onto (b) not one-one, but onto (c) one-one, but not onto (d) neither one-one, nor onto

The function f:[0,\ oo)->R given by f(x)=x/(x+1) is (a) one-one and onto (b) one-one but not onto (c) onto but not one-one (d) neither one-one nor onto

If f:NrarrN is given by f(x)={((x+1)/(2), if x " is odd"),((x)/(2),if x " is even"):} and g:NrarrN is given by g(x)=x-(-1)^x , then f(g(x)) is (a) one one and onto (b) many one and onto (c) one one and not onto (d) neither one-one onto

If f:[0,oo)->[0,oo) and f(x)=x/(1+x), then f(x) is (a) one-one and onto (b)one-one but not onto (c)onto but not one-one (d)neither on-one nor onto

Home
Profile