Respuesta :
The value of [tex]\boxed{{\mathbf{fog}}\left( {\mathbf{4}} \right){\mathbf{ is - 49}}}[/tex].
Further explanation:
A function is relation between two and more than two variables that assigns exactly one output to each input.
The set of all input values on the graph of the function is known as domain and the set of all the output values is known as the range of the function.
The composition of the function is to determine a function [tex]h\left( x \right)[/tex] by plugging the output value of [tex]g\left( x \right)[/tex] into [tex]f\left( x \right)[/tex] as input value.
The composite function [tex]h\left( x \right)[/tex] can be written as [tex]h\left( x \right) = \left( {fog} \right) = f\left( {g\left( x \right)} \right)[/tex].
Given:
The provided functions are [tex]f\left( x \right) = 3x - 7[/tex] and [tex]g\left( x \right) = - 2x - 6[/tex].
Step by step explanation:
Step 1:
First determine the composite function [tex]h\left( x \right) = f\left( {g\left( x \right)} \right)[/tex].
Substitute the given function [tex]g\left( x \right) = - 2x - 6[/tex] into the function [tex]f\left( x \right) = 3x - 7[/tex] as the input value to determine the composite function [tex]h\left( x \right)[/tex].
[tex]\begin{aligned}fog\left( x \right) &= f\left( {g\left( x \right)} \right)\\&= f\left( { - 2x - 6} \right) \\&= 3\left( { - 2x - 6} \right) - 7 \\&= - 6x - 25\\\end{aligned}[/tex]
Therefore, the value of [tex]fog\left( x \right) = - 6x - 25[/tex].
Step 2:
Now substitute the value [tex]x = 4[/tex] in the equation [tex]fog\left( x \right) = - 6x - 25[/tex] to obtain the value of [tex]fog\left( 4 \right)[/tex] as,
[tex]\begin{aligned}fog\left( 4 \right) &= - 6\left( 4 \right) - 25 \hfill\\fog\left( 4 \right)&= - 49 \hfill \\\end{aligned}[/tex]
Therefore, the value of [tex]fog\left( 4 \right){\text{ is }} - 49[/tex].
Learn more:
- Learn more about the function is graphed below https://brainly.com/question/9590016
- Learn more about the symmetry for a function https://brainly.com/question/1286775
- Learn more about midpoint of the segment https://brainly.com/question/3269852
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Function
Keywords: Composite function, transformation, sine, shifting, upward, addition, subtraction, trigonometric function, output value, reversed rule, basic function, horizontal line test.
The (f o g)(4) is -49.
Function
It is an expression, rule, or law that defines the relationship between one variable to another variable.
Given
f(x) = 3x - 7 and
g(x) = -2x - 6.
To find
Find (f o g)(4).
How to get (f o g)?
Let (f o g)(x)
then the (f o g)(x) can be written as
(f o g)(x) = f[g(x)]
That means g(x) becomes the variable for f(x)
f[ 3g(x)-7]
Put the value of g(x) in above equation then
[tex]\rm (f\ o\ g)(x) = 3(-2x-6) - 7\\ (f\ o\ g)(x) = -6x -18 -7 \\[/tex]
At x = 4 then
[tex]\rm (f\ o\ g)(4) = -6*4-18-7\\ (f\ o\ g)(4) = -24-18-7\\ (f\ o\ g)(4) = -49[/tex]
Thus the (f o g)(4) is -49.
More about the function link is given below.
https://brainly.com/question/5245372
