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In order to determine a function's inverse, solve for x and then switch the x and y.
`f(x) = 2x + 6`
Substitute y for f(x): `y = 2x + 6`
Solve for x.
`y = 2x + 6`
`y - 6 = 2x` Multiply by `1/2` to isolate x.
`1/2(y - 6) = x` Switch x and y.
`1/2(x-6) = y`
or `y = 1/2(x - 6)`
Since `g(x) = 1/2(x-6)` then the 2 functions are inverses.
Two functions f(x) and g(x) are inverse functions if the value of f(g(x)) = x.
For example consider a function f(x) = x + 2 and g(x) = x - 2
f((g(x)) = f(x - 2) = x - 2 + 2 = x
This holds for any function f(x) and its inverse `f^-1(x)` .
The value of `f(f^-1(x))` should always equal x.
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