Answer:
See below.
Step-by-step explanation:
Graphically: the graphs of a function and its inverse are symmetric with respect to the line y = x.
Algebraically: If functions f(x) and g(x) are inverses of each other, then the composition of f and g must equal x, and the composition of g and f must also equal x.
Two functions are inverse of each other:
An inverse function is defined as a function, which can reverse into another function.
For example,
[tex]f(x) = 3x - 2\\\\g(x) = \frac{x+2}{3}[/tex]
Checking if g(x) and f(x) are inverse of each other.
fog(x) = [tex]3(\frac{x+2}{3} )- 2 = x + 2 - 2 = x[/tex]
gof(x) = [tex]\frac{3x-2+2}{3} = x[/tex]
Since, fog(x) = gof(x) = x, it is algebraically verified that f(x) and g(x) are inverse of each other.
To prove that graphically, we plot the two functions.
As can be observed the two functions are symmetric to each other across the line y = x, thus, they are inverse of each other. (To check if the two functions are symmetric of each other, pick the graph of one function, for every point, interchange the x and y coordinates and plot them. The new graph will be of the inverse function.)
Learn more about inverse of a function here
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