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KCET2014MathematicsApplication of Derivatives

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)= )

Options

  1. A( 0- x -1 )
  2. B( x -1 )
  3. C( 1 (x+1)² x>-1 )
  4. D( x +1 )

Correct answer

B. ( x -1 )

Step-by-step solution

Given that f(x)=(x+1)² for x -1 and g(x) is the reflexion of f(x) in the line y=x , then g(x) is the inverse of f(x) Let y=(x+1)² y =x+1x= y -1 Now, f⁻¹(y)= y -1 or g(x)= x -1 Hence, the required function, g(x)= x -1

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