Home
Class 12
MATHS
Let f:R->R and g:R->R be two one-one and...

Let `f:R->R` and `g:R->R` be two one-one and onto functions such that they are mirror images of each other about the line `y=a`. If `h(x)=f(x)+g(x)`, then `h(x)` is (A) one-one onto (B) one-one into (D) many-one into (C) many-one onto

A

one -one and onto

B

only one-one and not onto

C

only onto but not one-one

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R.

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

f:R to R is a function defined by f(x)= 10x -7, if g=f^(-1) then g(x)=

Let the function f:R to R be defined by f(x)=cos x, AA x in R. Show that f is neither one-one nor onto.

The function f:[0,3] to [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

Show that an onto function f : {1, 2, 3} rarr {1, 2, 3} is always one-one.

Let f : R rarr R be defined as f(x) = 10 x +7 . Find the function g:R rarrR such that gof = fog = I_(g)

The function f : R -> R defined as f (x) =1/2 In (sqrt(sqrt(x^2+1)+x) + sqrt(sqrt(x^2+1)-x)) is (a)one-one and onto both (b)one-one but not onto (c)onto but not one-one (d)Neither one-one nor onto

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