The two compositions are: f( g(x) ) = x and g( f(x) ) = x
What is an inverse function?
The inverse function is defined as a function obtained by reversing the given function.
We have given functions :
f(x) = 4/5x + 1
g(x) = (5x - 5)/4
Let's check if the functions are inverses.
f( g(x) ) = 4/5g(x) + 1 = 4/5{(5x - 5)/4} + 1 = (x - 1) + 1 = x
g( f(x) ) = (f(x) - 1)5/4 = (4/5x + 1 - 1)5/4 = x
So, f(x) and g(x) are inverses.
Hence, the two compositions are: f( g(x) ) = x and g( f(x) ) = x
Learn more about inverse function here:
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