If f:R→R is an invertible function such that f(x) and f−1(x) are symmetric about the line y=−x, then
f(x) is odd
f(x) and f−1(x) may not be symmetric about the line y = x
f(x) may not be odd
f−1(x) may be odd
Since f(x) and f−1(x) are symmetric about the line y = -x
If α,β lies on y = f(x) then −α,−β lie on y=f−1(x)
⇒−α,−β lies on y=f(x)⇒y=f(x) is odd.