Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
Let f : R → R be any function. Define g : R → R by g (x) = ¦f (x) ¦for all x. Then g is : Onto if f is onto One-one is f one-one Continuous if, f is continuous Differentiable if f is differentiable
This can be simply explained through an example:
let f(x) = x so g(x) = |x|
so if f(x) is continuous and differentiable , then g(x) is continuous and differentiable too
and if f(x) is one-one function , then g(x)cant be one-one but g(x) will be an onto fuction or many to one function
and f(x) is onto , then g(x) will be an onto function too
--
regards
Ramesh
thats a shockingly atrocious reply by the expert
Its obvious that g(x) is non-negative. Hence for negative real values there is no x such that g(x) = y. So onto is ruled out.
Again if x and y are two real numbers such that f(x) = - f(y) we have g(x) = g(y) though x /= y . So one-one is out.
Continuous is right, as if a sequence {x} is convergent to l, {|x|} is convergent to |l|
Differentiability-the critical points are where f(x) = 0. If f(x) changes sign in an interval containing this point and if f'(x) /= 0 at this point then we have a point of non-differentiability.
Register Yourself for a FREE Demo Class by Top IITians & Medical Experts Today !