First slide

Functions (XII)

Question

If $R \to R$ is 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

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

f(x) may not be odd
D

none of these

Solution

Since $f (x) and f^{- 1} (x)$ are symmetric about the line y = x.
If $(α, β)$ lies on $y = f (x),$ then $(- α, - β)$ lies on $y = f^{- 1} (x) .$
$\begin{array}{l} Therefore, (- α, - β) lies on y = f (x) . \\ Hence, y = f (x) is odd . \end{array}$

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