Home
Class 12
MATHS
Prove that f: R->R , given by f(x)=2x , ...

Prove that `f: R->R` , given by `f(x)=2x` , is one-one and onto.

Text Solution

Verified by Experts

Here, `f(x) = 2x`
A function is a one-one function such that `f(x_1) = f(x_2)` only if `x_1 = x_2`.
Here, `f(x_1) = 2x_1`
`f(x_2) = 2x_2`
If `f(x_1) = f(x_2)`, then,
`2x_1 = 2x_2 => x_1 = x_2`
`:. f(x)` is one-one function.
...
Promotional Banner

Similar Questions

Explore conceptually related problems

Show that f: R->R , given by f(x)=x-[x] , is neither one-one nor onto.

Show that the function f: N->N , given by f(x)=2x , is one-one but not onto.

Show that the function f: N->N , given by f(x)=2x , is one-one but not onto.

Show that f: RvecR , given by f(x)=x-[x], is neither one-one nor onto.

Show that f: RvecR , given by f(x)=x-[x], is neither one-one nor onto.

Show that the modulus function f: R->R , given by f(x)=|x| is neither one-one nor onto.

Show that the exponential function f: R->R , given by f(x)=e^x , is one-one but not onto. What happens if the co-domain is replaced by R0+ (set of all positive real numbers).

Write whether f: R->R given by f(x)=x+sqrt(x^2) is one-one, many-one, onto or into.

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

Prove that the Greatest Integer Function f : R->R , given by f (x) = [x] , is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.