Answer :
To determine the domain of the function [tex]\( f(x) = -\frac{3}{6} \left( \frac{3}{5} \right) \)[/tex], follow these steps:
1. Simplify the Expression:
Start by simplifying the constant expression [tex]\( f(x) = -\frac{3}{6} \left( \frac{3}{5} \right) \)[/tex].
Simplify [tex]\(-\frac{3}{6}\)[/tex]:
[tex]\[ -\frac{3}{6} = -\frac{1}{2} \][/tex]
Then, multiply by [tex]\(\frac{3}{5}\)[/tex]:
[tex]\[ -\frac{1}{2} \times \frac{3}{5} = -\frac{1 \times 3}{2 \times 5} = -\frac{3}{10} \][/tex]
So, the function [tex]\( f(x) \)[/tex] simplifies to:
[tex]\[ f(x) = -\frac{3}{10} \][/tex]
2. Identify the Nature of the Function:
Notice that [tex]\( f(x) = -\frac{3}{10} \)[/tex] is a constant function. This means that the function's value does not depend on [tex]\( x \)[/tex].
3. Determine the Domain:
Since [tex]\( f(x) \)[/tex] is a constant function and does not depend on [tex]\( x \)[/tex], there are no restrictions on the values [tex]\( x \)[/tex] can take. The function is defined for all real numbers [tex]\( x \)[/tex].
Therefore, the domain of the function [tex]\( f(x) = -\frac{3}{10} \)[/tex] is:
All real numbers.
So, the correct answer is:
[tex]\[ \text{all real numbers} \][/tex]
1. Simplify the Expression:
Start by simplifying the constant expression [tex]\( f(x) = -\frac{3}{6} \left( \frac{3}{5} \right) \)[/tex].
Simplify [tex]\(-\frac{3}{6}\)[/tex]:
[tex]\[ -\frac{3}{6} = -\frac{1}{2} \][/tex]
Then, multiply by [tex]\(\frac{3}{5}\)[/tex]:
[tex]\[ -\frac{1}{2} \times \frac{3}{5} = -\frac{1 \times 3}{2 \times 5} = -\frac{3}{10} \][/tex]
So, the function [tex]\( f(x) \)[/tex] simplifies to:
[tex]\[ f(x) = -\frac{3}{10} \][/tex]
2. Identify the Nature of the Function:
Notice that [tex]\( f(x) = -\frac{3}{10} \)[/tex] is a constant function. This means that the function's value does not depend on [tex]\( x \)[/tex].
3. Determine the Domain:
Since [tex]\( f(x) \)[/tex] is a constant function and does not depend on [tex]\( x \)[/tex], there are no restrictions on the values [tex]\( x \)[/tex] can take. The function is defined for all real numbers [tex]\( x \)[/tex].
Therefore, the domain of the function [tex]\( f(x) = -\frac{3}{10} \)[/tex] is:
All real numbers.
So, the correct answer is:
[tex]\[ \text{all real numbers} \][/tex]
