Respuesta :
The domain of the function [tex]f\left( x \right) = 5x - 7[/tex] is all the real numbers.
Further explanation:
Domain is a set of all the possible values of the function. The value at which the function is defined is known as domain.
Range is a set of values that the function takes.
The output values of the function are known as range and the input values on which function is defined is known as the domain of the function.
Explanation:
The given function is [tex]f\left( x \right) = 5x - 7[/tex].
Consider the value of x less than zero.
Substitute -1 for x to check whether the function is defined.
[tex]\begin{aligned}f\left({ - 1}\right)&= 5\left({ - 1}\right)- 7\\&= - 5 - 7\\&= - 12\\\end{aligned}[/tex]
Consider the value of x greater than zero.
Substitute 1 for x to check whether the function is defined.
[tex]\begin{aligned}f\left( 1 \right)&= 5\left( 1 \right)- 7\\&=5 - 7\\&= - 2\\\end{aligned}[/tex]
The function [tex]f\left( x \right) = 5x - 7[/tex] is defined for all the value of x.
The input values are all the real numbers.
Hence, the domain of the function [tex]f\left( x \right) = 5x - 7[/tex] is all the real numbers.
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Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Functions
Keywords: range, domain, codomain, relation, function, graph, coordinates, close interval, open interval, values.
The domain of the given function is the set of all real numbers.
How to find the domain of a function?
We always start assuming that the domain of a function is the set of all real numbers, and then we start to remove the problematic points.
Where a problematic point is a value of x that causes a given problem in the function, an example of this can be in a function where a given value of x makes a denominator to become equal to zero, this is a problem because we can't divide by zero.
In this case, the function is:
f(x) = 5*x - 7
Here we don't have any denominator nor any sub-function that has problems in any value of x.
Thus, the domain of this function is the set of all real numbers.
If you want to learn more about domains, you can read:
https://brainly.com/question/1770447
