Maths-
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Question

Suppose f left parenthesis x right parenthesis equals left parenthesis x plus 1 right parenthesis squared forx 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–

  1. negative square root of x minus 1 comma x greater or equal than 0    
  2. fraction numerator 1 over denominator left parenthesis x plus 1 right parenthesis to the power of 2 end exponent end fraction comma x greater than negative 1    
  3. square root of x plus 1 end root comma x greater or equal than negative 1    
  4. square root of x minus 1 comma x greater or equal than 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 forx 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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