f(x) = 7x - 1
g(x) = (x - 1)/7
(f o g)(x)
= f(g(x))
= f((x - 1)/7)
= 7((x - 1)/7) - 1
= (x - 1) - 1
= x - 2
(g o f)(x)
= g(f(x))
= g(7x - 1)
= (7x - 1 - 1)/ 7
= (7x - 2)/7
For f(x) and g(x) to be inverses of each other, the condition that must be satisfied is
(f o g)(x) = (g o f)(x) = x
Since this condition is not satisfied in this case
Therefore, f(x) and g(x) are not inverses of each other.
Use the composition of functions to determine if f(x) and g(x) are inverses of one another....
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