Respuesta :
Answer:
Yes f(x) and g(x) are the inverse function.
Step-by-step explanation:
Given : [tex]f(x)=\frac{7x-2}{4}[/tex] and [tex]g(x)=\frac{7x-2}{4}[/tex]
To find : whether they are inverse or not.
Solution : First we find the inverse of f
[tex]y=\frac{7x-2}{4}[/tex]
Interchange x and y
[tex]x=\frac{7y-2}{4}[/tex]
Solve for y
[tex]4x=7y-2[/tex]
[tex]\rightarrow 4x+2=7y[/tex]
[tex]\rightarrow\frac{4x+2}{7}=y[/tex]
[tex]\rightarrow\frac{4x+2}{7}=g(x)[/tex]
Hence, f(x) and g(x) are the inverse function.
They are algebraically inverse functions.
Function
The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
Given
[tex]\rm f(x ) =\dfrac{7x-2}{4}\ \ \ and \ \ g(x) = \dfrac{4x+2}{7}[/tex] are the two functions.
To find
They determine algebraically whether or not.
How to determine algebraically whether or not?
[tex]\rm f(x ) =\dfrac{7x-2}{4}\ \ \ and \ \ g(x) = \dfrac{4x+2}{7}[/tex] are the two functions.
Let [tex]\rm y =\dfrac{7x-2}{4}[/tex], then interchange the variables x and y.
[tex]\begin{aligned} \rm x &=\dfrac{7y-2}{4}\\\\4x &= 7y-2\\\\4x+ 2 &= 7y\\\\y &= \dfrac{4x+2}{7} \\\end{aligned}[/tex]
So here y is equal to g(x).
Thus they are algebraically inverse functions.
More about the function link is given below.
https://brainly.com/question/5245372
