Assertion :If f(x+y)+f(x−y)=2f(x)f(y)∀x,y∈R and f(0)≠0, then f(x) is an even function. Reason: If f(−x)=f(x), then f(x) is even
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
Assertion is correct but Reason is incorrect
Both Assertion and Reason are incorrect
A
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
B
Assertion is correct but Reason is incorrect
C
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
D
Both Assertion and Reason are incorrect
Open in App
Solution
Verified by Toppr
Given f(x+y)+f(x−y)=2f(x)f(y)...(i)
Was this answer helpful?
0
Similar Questions
Q1
Assertion :If f(x+y)+f(x−y)=2f(x)f(y)∀x,y∈R and f(0)≠0, then f(x) is an even function. Reason: If f(−x)=f(x), then f(x) is even
View Solution
Q2
Assertion: All the points (1, 0), (-1, 0), (2, 0) and (5, 0) lie on the x – axis.
Reason: Equation of the x – axis is y = 0 Now, choose the correct option.
View Solution
Q3
Assertion: In the equation, y=Asin(kx−ωt) , particle starts from its mean position x=0 and moves towards negative y−axis. Reason: The wave corresponding to given equation is travelling towards positive x−direction.
View Solution
Q4
Assertion: The compressibility factor for H2 and He is (1+PbRT) Reason: The compressibility factor for H2 and He can be derived from Van der Waal's equation.
View Solution
Q5
Assertion – The non-fusible impurities present in iron ore are removed by CaCO3 .
Reason: CaCO3 which decomposes into CaO and CO2. The CaO formed reacts with SiO2 to remove silica