Suppose f(x)=(x+1)^(2) for x >= -1 . if g(x) is the function -Turito

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Question

Suppose $f left parenthesis x right parenthesis equals left parenthesis x plus 1 right parenthesis squared$ for $x greater or equal than negative 1$ . 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–

$- \sqrt{x} - 1, x \geq 0$
$\frac{1}{(x + 1)^{2}}, x > - 1$
$\sqrt{x + 1}, x \geq - 1$
$\sqrt{x} - 1, x \geq 0$

Hint:

g(x) is reflection of f(x) in line y = x
We have to find $f to the power of negative 1 end exponent left parenthesis x right parenthesis$

The correct answer is: $square root of x minus 1 comma x greater or equal than 0$

Given : $f left parenthesis x right parenthesis equals left parenthesis x plus 1 right parenthesis squared$
Let y = f(x)
y = ( $x space plus 1 right parenthesis squared$
x +1 = $plus-or-minus square root of y$
$x space equals space plus-or-minus square root of y space minus 1$
We have been given that $f left parenthesis x right parenthesis equals left parenthesis x plus 1 right parenthesis squared$ for $x greater or equal than negative 1$
$rightwards double arrow x space equals space plus square root of y space minus 1$
Since y = f(x)
$rightwards double arrow f to the power of negative 1 end exponent left parenthesis y right parenthesis space equals space x rightwards double arrow f to the power of negative 1 end exponent left parenthesis y right parenthesis space space equals space square root of y space minus 1 rightwards double arrow f to the power of negative 1 end exponent left parenthesis x right parenthesis space equals space square root of x space minus 1 S i n c e comma space g left parenthesis x right parenthesis space i s space r e f l e c t i o n space o f space f left parenthesis x right parenthesis space i n space l i n e space y space equals space x g left parenthesis x right parenthesis space equals space square root of x space minus 1 space comma space x greater or equal than 0$

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Question

Suppose $f left parenthesis x right parenthesis equals left parenthesis x plus 1 right parenthesis squared$ for $x greater or equal than negative 1$ . 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–

$- \sqrt{x} - 1, x \geq 0$
$\frac{1}{(x + 1)^{2}}, x > - 1$
$\sqrt{x + 1}, x \geq - 1$
$\sqrt{x} - 1, x \geq 0$

Hint:

Answer

The correct answer is: $square root of x minus 1 comma x greater or equal than 0$

Solution

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Question

Suppose for. 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–

Hint:

Answer

The correct answer is:

Solution

Given : Let y = f(x)y = (x +1 = We have been given that forSince y = f(x)

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Suppose $f left parenthesis x right parenthesis equals left parenthesis x plus 1 right parenthesis squared$ for $x greater or equal than negative 1$ . 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–

The correct answer is: $square root of x minus 1 comma x greater or equal than 0$