Home
Class 12
MATHS
Let f be a differential function such th...

Let f be a differential function such that `f(x)=f(2-x)` and `g(x)=f(1 +x)` then (1) g(x) is an odd function (2) g(x) is an even function (3) graph of f(x) is symmetrical about the line x= 1 (4) `f'(1)=0`

A

g(x) is an odd function

B

g(x) is an even function

C

graph of `f(x)` is symmetrical about the line x = 1

D

`f'(1)=0`

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
We have `f(x)=f(2-x)`
Replacing x by `f(1+x)`, we get
`f(1+x)=f(1-x)`
Hence graph of f(x) is symmetrical about the line x = 1.
Also `g(x)=f(1+x)=f(1-x)=g(-x)`
`therefore` g(x) is an even function.
Further `f'(1+x)=-f'(1-x)`
`therefore" "f'(1)=-f'(1)`
`therefore" "f'(1)=0`
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    CENGAGE PUBLICATION|Exercise Comprehension Type|7 Videos

  • FUNCTIONS

    CENGAGE PUBLICATION|Exercise Comprehension Type|7 Videos

  • EQUATION OF PLANE AND ITS APPLICATIONS -II

    CENGAGE PUBLICATION|Exercise DPP 3.4|8 Videos

  • GETTING STARTED WITH GRAPHS

    CENGAGE PUBLICATION|Exercise Exercises 1.18|1 Videos

Similar Questions

Explore conceptually related problems

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1) =1 , then

If f(x) is a function such that f'(x)=(x-1)^(2)(4-x) then,

Let f be a differentiable function such that f(1) = 2 and f'(x) = f (x) for all x in R . If h(x)=f(f(x)) , then h'(1) is equal to

Let f be a twice differentiable function such that f"(x) = -f(x) , and f'(x) = g(x) , h(x)=[f(x)]^2+[g(x)]^2 Find h(10), if h(5) = 11

If f: R->R is an odd function such that f(1+x)=1+f(x) and x^2f(1/x)=f(x),x!=0 then find f(x)dot

If f(x) is a function such that f'(x)= (x-1)^2 (4-x) , then

Let f(x) be real valued and differentiable function on R such that f(x+y)=(f(x)+f(y))/(1-f(x)dotf(y)) f(x) is Odd function Even function Odd and even function simultaneously Neither even nor odd

Let a function f(x), x ne 0 be such that f(x)+f((1)/(x))=f(x)*f((1)/(x))" then " f(x) can be

If f is a twice differentiable function such that f''(x)=-f(x),f'(x)=g(x) ,h(x)=[f(x)]^2+[g(x)]^2 if h(5)=11, then h(10) equals

Let f:(-pi/2,pi/2)vecR be given by f(x)=(log(sec"x"+tan"x"))^3 then f(x) is an odd function f(x) is a one-one function f(x) is an onto function f(x) is an even function