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 ≤-1 then f (24) is equal to

Question

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 ≤-1 then f (24) is equal to (A) -4 (B) 4 (C) -6 (D) 6

Tardigrade Admin · Accepted Answer

Clearly f ( x ) is inverse of g ( x ) g ( x )= f -1( x ) ⇒ f ( x )= g -1( x ) g ( x )=24 ⇒( x +1)2-1=24 ⇒ x +1=-5= x =-6 ∴ g (-6)=24 ⇒ g -1(24)= f (24)=-6

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

-4

4

-6

6

Clearly $f (x)$ is inverse of $g (x)$
$g (x) = f^{- 1} (x) \Rightarrow f (x) = g^{- 1} (x)$
$g (x) = 24 \Rightarrow (x + 1)^{2} - 1 = 24$
$\Rightarrow x + 1 = - 5 = x = - 6$
$∴ g (- 6) = 24 \Rightarrow g^{- 1} (24) = f (24) = - 6$

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≤−1 then f(24) is equal to

-4

4

-6

6

Clearly f(x) is inverse of g(x) g(x)=f−1(x)⇒f(x)=g−1(x) g(x)=24⇒(x+1)2−1=24 ⇒x+1=−5=x=−6 ∴g(−6)=24⇒g−1(24)=f(24)=−6

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

Clearly $f (x)$ is inverse of $g (x)$
$g (x) = f^{- 1} (x) \Rightarrow f (x) = g^{- 1} (x)$
$g (x) = 24 \Rightarrow (x + 1)^{2} - 1 = 24$
$\Rightarrow x + 1 = - 5 = x = - 6$
$∴ g (- 6) = 24 \Rightarrow g^{- 1} (24) = f (24) = - 6$