To determine the domain of the given function [tex]\( f(x) = 15x + 35 \)[/tex], we need to identify all possible values of [tex]\( x \)[/tex] that can be input into the function without causing any issues such as division by zero or taking the square root of a negative number.
Given that [tex]\( f(x) = 15x + 35 \)[/tex] is a linear function, let's examine its form:
1. The function [tex]\( f(x) = 15x + 35 \)[/tex] is a linear equation.
2. Linear equations of the form [tex]\( ax + b \)[/tex], where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are constants, do not have any restrictions on the values that [tex]\( x \)[/tex] can take. This is because linear functions are defined for all real numbers.
Therefore, the domain of the function [tex]\( f(x) = 15x + 35 \)[/tex] is all real numbers.
To summarize:
- Linear functions are continuous and defined for every possible input value.
- There are no values of [tex]\( x \)[/tex] that would make the expression [tex]\( 15x + 35 \)[/tex] undefined.
Hence, the domain of [tex]\( f(x) = 15x + 35 \)[/tex] is all real numbers.
The correct choice is:
[tex]\[ \text{all real numbers} \][/tex]
