The domain f the function is (-∞, 1/3) U (1/3, ∞)
Composite functions
The composite functions are also known as function of a function
Given the following functions
f(x) = √2-6x
g(x) = -1/x
In order to determine the composite function g(f(x))
g(f(x)) = g(√2-6x)
Replace x with √2-6x in g(x)
g(f(x)) = -1/√2-6x
The expression does not exist when √2-6x = 0
2-6x = 0
x = 1/3
The values shows that the domain of the function exists on all real numbers except 1/3.
Hence the domain f the function is (-∞, 1/3) U (1/3, ∞)
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