Home
Class 12
MATHS
Show that the modulus function f: R rarr...

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

Text Solution

Verified by Experts

`f(-2) = |-2| = 2` and
`f(2) = |2| = 2`, f maps both -2 and 2 to 2
`therefore` f is not one-one
Since `|x|` assumes only non-negative real values, negative real numbers can.t have pre-images
`therefore` f is not onto
Promotional Banner

Similar Questions

Explore conceptually related problems

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

Prove that the function f: R rarr R given by f(x)=2 x is one-one and onto.

Show that the function f:R rarr R given by f(x)=x^3 is injective.

Show that the function f : R_** rarr R_** defined by f (x) = 1/x is one-one and onto,where R_** is the set of all non-zero real numbers. Is the result true, if the domain R_** is replaced by N with co-domain being same as R_** ?

Draw the graph of the function f: R rarr R defined by f(x)=x^3, x in R .

Prove that the function f: N rarr N , defined by f(x)=x^2+x+1 is one-one but not onto.

Show that the function given by f(x)=sinx is neither increasing nor decreasing in (0,pi)

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