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

one-one

into

onto

many one

Text Solution

Verified by Experts

The correct Answer is:

B, D

Topper's Solved these Questions

RELATION, FUNCTION & ITF
RESONANCE|Exercise COMPREHENSION_TYPE|6 Videos
RELATION, FUNCTION & ITF
RESONANCE|Exercise JEE ADVANCED|14 Videos
RELATION, FUNCTION & ITF
RESONANCE|Exercise INTEGER_TYPE|21 Videos
NUMBER THEORY
RESONANCE|Exercise Exercise -2 (PART - II)|4 Videos
SEQUENCE & SERIES
RESONANCE|Exercise EXERCISE -2 (PART-II : PREVIOUSLY ASKED QUESTION OF RMO)|3 Videos

Similar Questions

Explore conceptually related problems

Let f:R rarr R and g:R rarr 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

Let f: RrarrRa n dg: RrarrR be two one-one and onto function such that they are the mirror images of each other about the line y=a. If h(x)=f(x)+g(x),t h e nh(x) is (a)one-one and onto (b)only one-one and not onto (c)only onto but not one-one (d)neither one-one nor onto

f:[-1,1]rarr[-1,2]f(x)=x+|x|, is (1) one-one onto (2) one-one into (3) many one onto (4) many one into

Let f:R rarr R, be defined as f(x)=e^(x^(2))+cos x, then is (a) one-one and onto (b) one-one and into ( c) many-one and onto (d) many-one and into

f(x) is a polynomial function, f: R rarr R, such that f(2x)=f'(x)f''(x). f(x) is (A) one-one and onto (B) one-one and into (C) many-one and onto (D) many-one and into

f: N rarr N, where f(x)=x-(-1)^(x) .Then f is: (a)one-one and into (b)many-one and into (c)one-one and onto (d)many-one and onto

One-one,many-one, into and onto function

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: 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

f:R^(+)rarr[2,oo] and f(x)=2+3x^(2), then f(x) is (i)one-one (ii)into (iii)many-one (iv) onto

RESONANCE-RELATION, FUNCTION & ITF-MCQ_TYPE

If f(x)={(x^(2),xle1),(1-x,xgt1):} & composite function h(x)=|f(x)|+f(...
Text Solution
|
Let f(x)={0 for x=0 x^2 sin (pi/x) for -1 < x < 1(x != 0), then : x |...
Text Solution
|
If g:[-2,2]vecR , where f(x)=x^3+tanx+[(x^2+1)/P] is an odd function, ...
Text Solution
|
If f:Rto[-1,1] where f(x)=sin((pi)/2[x]), (where [.] denotes the great...
Text Solution
|
If f(x)=(2x(sinx+tanx))/(2[(x+2pi)/(pi)]-3) then it is (where [.] deno...
Text Solution
|
Identify the statement(s) which is/are incorrect?
Text Solution
|
If F(x)=(sinpi[x])/({x}) then F(x) is (where {.} denotes fractional pa...
Text Solution
|
Let f:R->R and g:R->R be two one-one and onto functions such that they...
Text Solution
|
Which of the following pairs of functions are identical?
Text Solution
|
Q. if sin^-1 x+sin^-1 y+sin^-1 z=(3pi)/2, then
Text Solution
|
If x=cos e c[tan^(-1){"cos"(cot^(-1)(sec(sin^(-1)a)))}] and y-"sec"[co...
Text Solution
|
If alpha satisfies the inequation x^2 - x - 2 > 0, then a value exists...
Text Solution
|
For the finuction f(x)=ln (sin^-1 log2 x)
Text Solution
|
If the following functions are defined from [-1,1]to[-1,1], select tho...
Text Solution
|
The expression 1/(sqrt(2)){(sincot^(- 1)costan^(- 1)t)/(costan^(- 1)si...
Text Solution
|
If 0< x< 1,then tan^(-1)(sqrt(1-x^2)/(1+x)) is equal to
Text Solution
|
If f(x)=cos^(- 1)x+cos^(- 1){x/2+1/2sqrt(3-3x^2)}then
Text Solution
|
sum(n=1)^oo(tan^-1((4n)/(n^4-2n^2+2))) is equal to (A) tan ^-1 (2)+t...
Text Solution
|
If sin^2 (2 cos^-1 (tan x)) = 1 then x may be
Text Solution
|
If sin^-1 x + 2 cot^-1 (y^2-2y) = 2pi, then
Text Solution
|