Respuesta :
Answer:
The correct option is C) [tex]f(x)=4x \ \text{and} \ g(x)=\frac{x}{4}[/tex]
Step-by-step explanation:
We need to find out the pair of functions which are inverse of each other
A) [tex]f(x)=x \ \text{and} \ g(x)=-x[/tex]
Since, [tex](fog)(x)=f(g(x))=-x[/tex]
and [tex](gof)(x)=g(f(x))=-x[/tex]
So, these are not inverse of each others
B) [tex]f(x)=2x \ \text{and} \ g(x)=\frac{-x}{2}[/tex]
Since, [tex](fog)(x)=f(g(x))=2(\frac{-x}{2})=-x[/tex]
and [tex](gof)(x)=g(f(x))=\frac{-2x}{2}=-x[/tex]
So, these are not inverse of each others
C) [tex]f(x)=4x \ \text{and} \ g(x)=\frac{x}{4}[/tex]
Since, [tex](fog)(x)=f(g(x))=4(\frac{x}{4})=x[/tex]
and [tex](gof)(x)=g(f(x))=\frac{4x}{4}=x[/tex]
So, these are inverse of each others
D) [tex]f(x)=-8x \ \text{and} \ g(x)=8x[/tex]
Since, [tex](fog)(x)=f(g(x))=-8(8x)=-64x[/tex]
and [tex](gof)(x)=g(f(x))=8(-8x)=-64x[/tex]
So, these are not inverse of each others
Therefore the correct option is C) [tex]f(x)=4x \ \text{and} \ g(x)=\frac{x}{4}[/tex]
The two function that are inverses of each other are
f(x) = 4x, g(x) = 1/4x
Option C
Given :
A set of functions and their inverses. we need to find which function is inverse to each other
When the function are inverses to each other then
f(g(x))= g(f(x))= x
Lets check each option
A) f(x) = x, g(x) = –x
[tex]f(g(x))=f(-x)=-x[/tex]
So they are not inverse to each other
B)f (x) = 2x, g(x) = -1/2x
[tex]f(g(x))=f(\frac{-1}{2}x)=2(\frac{-1}{2} x)=-x[/tex]
so, they are not inverse of each other
C) f(x) = 4x, g(x) = 1/4x
[tex]f(g(x))=f(\frac{1}{4}x)=4(\frac{1}{4}x)=x\\g(f(x))= g(4x)=\frac{1}{4}(4x)=x[/tex]
f(g(x))=g(f(x))=x
So, they are inverse of each other
D)f(x) = –8x, g(x) = 8x
[tex]f(g(x))=f(8x)=-8(8x)=-64x[/tex]
They are not inverse of each other
The two function that are inverses of each other are
f(x) = 4x, g(x) = 1/4x
Learn more :
brainly.com/question/18707215
