First slide

Functions (XII)

Question

If $f : R \to R$ is an invertible function such that f(x) and $f^{- 1} (x)$ are symmetric about the line $y = - x,$ then

Moderate

A

$f (x)$ is odd
B

$f (x) a n d f^{- 1} (x)$ may not be symmetric about the line y = x
C

$f (x)$ may not be odd
D

$f^{- 1} (x)$ may be odd

Solution

Since $f (x) a n d f^{- 1} (x)$ are symmetric about the line y = -x
If $(α, β)$ lies on y = f(x) then $(- α, - β)$ lie on $y = f^{- 1} (x)$
$\Rightarrow (- α, - β)$ lies on $y = f (x) \Rightarrow y = f (x)$ is odd.

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