Given below are two statements. Consider the function f(x) satisfying the relation…
Mathematics · JEE Main · NTA Exams — Sets, Relations and Functions
Consider the function f(x) satisfying the relation \(f(x+1)+f(x+7)=0 \quad \forall x \in R\).
Statement - 1: The possible least value of t for which \(\int_{a}^{a+t} f(x) d x\) is independent of a is 12.
Statement - 2: f(x) is a periodic function.
In the light of the above statements, choose the correct answer from the options given below:
Both the statements are true and Statement - 2 is the correct explanation of Statement - 1
Both the statements are true but Statement - 2 is not a correct explanation of Statement - 1
Statement - 1 is true and Statement - 2 is false
Statement - 1 is false and Statement - 2 is true
Answer
(A) Both the statements are true and Statement - 2 is the correct explanation of Statement - 1
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- If f(x)= [a-x^ n ]^ 1 / n , where a>0 and n is a positive integer, then f^ f [f( x )] is equal to:
- Let f(x)=x^ 3 +3 be bijective function, find its inverse
- The domain of function y= _ 10 _ 10 _ 10 _ 10 (up to n terms) is
- Let the function f. g. h are defined from the set of real numbers R to R such that f(x)=x^ 2 -1 g(x) = (x^ 2…
- If A = 1, 3, 5, 7, 9, 11, 13, 15, 17 , B = 2, 4, .......,18 and N is the universal set, then A c ((A B) B c )…
- Given the sets A = 1, 2, 3 , B = 3, 4 , C = 4, 5, 6 , then is
- The range of the function f( x )= x ^ 2 + 1 x ^ 2 +1
- Considering only the principal values of inverse trigonometric functions, the number of positive real values…
More Sets, Relations and Functions questions · Browse all practice questions