AP EAMCET202124 Aug 2021Morning ShiftMathematicsFunctionsActual
Which of the following is false?
Options
- AIf f is an even function from R to R , then f(0) must be equal to 0 .
- Bf: R R defined by f(x)=x-[x], x R , where [x] is the greatest integer not greater than x , is a periodic funct
- CIf f: R R is an odd function, then f(0)=0
- DNumber of onto functions from 1,2,3,4,5,6 to 1,2 is 62
Correct answer
A. If f is an even function from R to R , then f(0) must be equal to 0 .
Step-by-step solution
(a) If f is an even function from R to R , then f(0) must be equal to 0 . We know that if a function f(x) is even, then f(-x)=f(x) Now, if we assume f(x)= x aligned f(-x) & = (-x) & = x & =f(x) aligned (- )=( ) f(x)= x is an even function. Now, f(0)= 0=1 0 The given statement is false. (b) f: R R, f(x)=x-[x] We know that, x=[x]+ x where x = fractional part function aligned & x-[x]= x & f(x)= x & aligned where x is a periodic function. f(x) is periodic function. The given statement is true. (c) f: R R is an odd func