Mathematics
Grade10
Easy

Question

What is the inverse of the function f left parenthesis x right parenthesis equals 1 fourth x squared ?

  1. f to the power of negative 1 end exponent left parenthesis x right parenthesis equals 2 square root of x
  2. f to the power of negative 1 end exponent left parenthesis x right parenthesis equals square root of 2 x end root
  3. f to the power of negative 1 end exponent left parenthesis x right parenthesis equals 4 square root of x
  4. f to the power of negative 1 end exponent left parenthesis x right parenthesis equals 2 x

hintHint:

In this question we have to find the inverse of the given function  f left parenthesis x right parenthesis equals 1 fourth x squared or,y equals 1 fourth x squared for this we first switch x and y then obtain the value of y in terms of x.

The correct answer is: f to the power of negative 1 end exponent left parenthesis x right parenthesis equals 2 square root of x


    Given function  f left parenthesis x right parenthesis equals 1 fourth x squared
    Let  y equals 1 fourth x squared
    Switch x and  y
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x equals 1 fourth y squared end cell row cell 4 x equals y squared end cell row cell square root of 4 x end root equals y end cell row cell 2 square root of x equals y end cell end table
    So, the inverse of the function f to the power of negative 1 end exponent left parenthesis x right parenthesis equals 2 square root of x

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