Solve
Guides
0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Standard XII
Maths
Question

which of the following is an even function
  1. ax+a−xax−a−x
  2. f(x)=xax−1a−x+1
  3. f(x)=log2(x+√x2+1)
  4. f(x)=ax+1ax−1

A
f(x)=ax+1ax−1
B
f(x)=log2(x+√x2+1)
C
f(x)=xax−1a−x+1
D
ax+a−xax−a−x
Open in App
Solution
Verified by Toppr

Consider the given expression,

x(ax−1)(a−x+1)

Replace x by –x , we get,

=−x(a−x−1)(a−(−x)+1)$

=−x(1ax−1)(1ax+1)=x(1−axax)(1+axax)

=−x(1−ax)1+ax=−x(−(−1+ax))1+ax

=x(ax−1)1+ax


=x(ax−1)(a−x+1) is the even function.

Option (c) is correct answer

Was this answer helpful?
4
Similar Questions
Q1
Is the function f(x)=x(ax+1)ax−1 odd or even
View Solution
Q2
Determine whether the following is even or odd
f(x)=x(ax+1ax−1)
View Solution
Q3

How many of the following functions are even [sin x is odd and cosx is even]

(a) f(x) = x2|x| (b) f(x) = ex+e−x

(c) f(x) = log[1−x1+x] (d) log(√x2+1- x)

(e) f(x) = log(x + √x2+1 (f) ax−a−x

(g) f(x) = sinx+cosx (h) sinx×(ex−e−x)


___
View Solution
Q4

How many of the following functions are even [sin x is odd and cosx is even]

(a) f(x) = x2|x| (b) f(x) = ex+e−x

(c) f(x) = log[1−x1+x] (d) log(√x2+1- x)

(e) f(x) = log(x + √x2+1 (f) ax−a−x

(g) f(x) = sinx+cosx (h) sinx×(ex−e−x)


___
View Solution
Q5

A function f(x) is defined as
f(x)=⎧⎪⎨⎪⎩ax−bx≤13x,1<x<2bx2−ax≥2 is continuous at
x=1,2 then:

View Solution