Suppose f ( x ) = ( x + 1 ) 2 for x - 1 . If g ( x ) is the function whose graph is the reflection of the graph of f ( x ) with respect to the line y = x , then g ( x ) equals [2002]

Question

Suppose $f (x) = {(x + 1)}^{2}$ for $x \geq - 1 .$ If $g (x)$ is the function whose graph is the reflection of the graph of $f (x)$ with respect to the line $y = x$ , then $g (x)$ equals [2002]

Smart Achievers · Accepted Answer

(4)

$Given: f (x) = {(x + 1)}^{2}, x \geq - 1$

If $g (x)$ is the reflection of $f (x)$ in the line $y = x$ , then it can be obtained by interchanging $x$ and $y$ in $f (x)$

i.e., $y = {(x + 1)}^{2}$ changes to $x = {(y + 1)}^{2}$

$\Rightarrow y + 1 = \sqrt{x}$ $[y + 1 \neq - \sqrt{x}, since y \geq - 1]$

$\Rightarrow y = \sqrt{x} - 1,$ $defined ∀ x \geq 0$

$∴$ $g (x) = \sqrt{x} - 1,$ $\forall x \geq 0$

Solution

Q.
Suppose $f (x) = {(x + 1)}^{2}$ for $x \geq - 1 .$ If $g (x)$ is the function whose graph is the reflection of the graph of $f (x)$ with respect to the line $y = x$ , then $g (x)$ equals [2002]

1 $- \sqrt{x} - 1, x \geq 0$

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

3 $\sqrt{x + 1}, x \geq - 1$

4 $\sqrt{x} - 1, x \geq 0$

Want Us to Email you About Special Offers & Updates?

Solution

Q. Suppose f(x)=(x+1)2 for x≥-1. If g(x) is the function whose graph is the reflection of the graph of f(x) with respect to the line y=x, then g(x) equals [2002]

1 -x-1, x≥0

2 1(x+1)2, x>-1

3 x+1, x≥-1

4 x-1, x≥0