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Q.
If graph of $y=f(x)$ is reflection of graph of $y=g(x)$ w.r.t. line $y=x$ and $g(x)=(x+1)^2-1, x \leq-1$ then $f (24)$ is equal to
Relations and Functions - Part 2
Solution:
Clearly $f ( x )$ is inverse of $g ( x )$
$g ( x )= f ^{-1}( x ) \Rightarrow f ( x )= g ^{-1}( x ) $
$g ( x )=24 \Rightarrow( x +1)^2-1=24 $
$\Rightarrow x +1=-5= x =-6$
$\therefore g (-6)=24 \Rightarrow g ^{-1}(24)= f (24)=-6$