Mathematics
Grade10
Easy

Question

Identify the rule and the domain for straight f over straight g when f(x) = 5x- 6x , g (x) = 3x

  1. fraction numerator 5 straight x space minus space 6 over denominator 3 end fraction space comma straight D space colon space straight x space not equal to space 0 space comma space straight x space not equal to space 6 over 5
  2. fraction numerator 5 straight x minus 6 over denominator 3 end fraction , D : set of all real numbers
  3. 5x - 2 , D : set of all real numbers
  4. 5x - 2 , D :  x ≠ 2 over 5

Hint:

First, we need to find the function for which we have to find domain. The function is f over g left parenthesis x right parenthesis for which we will divide the functions.

The correct answer is: fraction numerator 5 straight x space minus space 6 over denominator 3 end fraction space comma straight D space colon space straight x space not equal to space 0 space comma space straight x space not equal to space 6 over 5


    Given f(x) = 5x2 - 6x , g(x) = 3x
    open parentheses straight f over straight g close parentheses left parenthesis straight x right parenthesis equals fraction numerator straight f left parenthesis straight x right parenthesis over denominator straight g left parenthesis straight x right parenthesis end fraction equals fraction numerator 5 straight x squared minus 6 straight x over denominator 3 straight x end fraction equals fraction numerator straight x left parenthesis 5 straight x minus 6 right parenthesis over denominator 3 straight x end fraction equals fraction numerator 5 straight x minus 6 over denominator 3 end fraction
    Domain is the set of all real numbers x such that x ≠ 0 , x ≠ 6 over 5.

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