Suppose f(x) = (x + 1)2 for x ≥ - 1. If g(x) is a function whose graph is the reflection of the graph of f(x) in the line y = x, then g(x) =

Question

Suppose f(x) = (x + 1)2 for x ≥ - 1. If g(x) is a function whose graph is the reflection of the graph of f(x) in the line y = x, then g(x) = (A) -√ x-1 (B) √ x-1 (C)  (1/(x+1)2)x>-1 (D) √x+1

Tardigrade Admin · Accepted Answer

Given, f(x)=(x+1)2, x ≥-1 and g(x) is reflection of graph f(x) in the line Y=x, then g(x) is the inverse of f(x). Let y=(x+1)2 ⇒ √Y=x+1 (taking square root) ⇒ x=√y-1 i.e., f-1(y)=√y-1 or g(x)=√x-1

Q. Suppose $f (x) = (x + 1)^{2}$ for $x \geq - 1$ . If $g (x)$ is a function whose graph is the reflection of the graph of $f (x)$ in the line $y = x$ , then $g (x) =$

$- x - 1$

$x - 1$

$\frac{1}{( x + 1 ) ^{2}} x > - 1$

$x + 1$

Given, $f (x) = (x + 1)^{2}, x \geq - 1$
and $g (x)$ is reflection of graph $f (x)$ in the line $Y = x$ ,
then $g (x)$ is the inverse of $f (x)$ .
Let $y = (x + 1)^{2}$
$\Rightarrow Y = x + 1$ (taking square root)
$\Rightarrow x = y - 1$
i.e., $f^{- 1} (y) = y - 1$
or $g (x) = x - 1$

Q. Suppose f(x)=(x+1)2 for x≥−1. If g(x) is a function whose graph is the reflection of the graph of f(x) in the line y=x, then g(x)=

−x​−1

x​−1

(x+1)21​x>−1

x​+1