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Mathematics

Grade10

Easy

Question

Identify the rule and the domain for $straight f over straight g$ when f(x) = 5x²- 6x , g (x) = 3x

$\frac{5 x - 6}{3}, D : x \neq 0, x \neq \frac{6}{5}$
$\frac{5 x - 6}{3}$ , D : set of all real numbers
5x - 2 , D : set of all real numbers
5x - 2 , D : x ≠ $\frac{2}{5}$

hint 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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