part test 1 doubt.............
Q2)
A Function can be written as the sum of even and odd function
a) Only if Function is continuous
b) If the function is continuous and Differentiable
c) If the function has a symmetric domain around origin
d) Statement is always true!
till now i thought the answer was D...........
but in d solution given by targetiit its given as C....
isnt d ans D??
1ok dude.......... logic is ok......................
and in d pic which i gave is d point C correct???? tht is even func has no inverse??????
wel wat bout cosx??? cos-1x exists naa???
did they mean only in d domain??
1well, posting the logic again.
to decide whether a function is even or odd, we check whether f(-x) = f(x) or -f(x) right.! hence if x ε {domain} implies -x (must also)ε {domain}.
and for ur second question.
i think the statement is regarding domain. inverse of an even function exists but domain will not be the same. for example f(x)=x2 → f-1(x) = ± √x . domain for f(x) is R while for f-1(x)=R+
let me know if i'm wrong for the second one !