Mathematics
Grade10
Easy

Question

Write an equation that represents the inverse of f left parenthesis x right parenthesis equals 3 x space minus space 5

  1. f to the power of negative 1 end exponent left parenthesis x right parenthesis equals 3 left parenthesis x space plus space 5 right parenthesis
  2. f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 5 space minus space x over denominator 3 end fraction
  3. f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x space minus space 5 over denominator 3 end fraction
  4. f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x space plus space 5 over denominator 3 end fraction

hintHint:

In this question we have to find the inverse function of the given function f left parenthesis x right parenthesis equals 3 x space minus space 5 or, y equals 3 x space minus space 5 for this we will first switch x and y and then obtain y in terms of x. The obtained function is the inverse function.

The correct answer is: f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x space plus space 5 over denominator 3 end fraction


    Given function  f left parenthesis x right parenthesis equals 3 x space minus space 5
    Let  y equals 3 x space minus space 5
    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 3 y space minus space 5 end cell row cell x space plus space 5 equals 3 y end cell row cell fraction numerator x space plus space 5 over denominator 3 end fraction 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 fraction numerator x space plus space 5 over denominator 3 end fraction

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