The pair of functions are f(g(x)) = √(x² + 1) +4 and g(f(x)) = x² + 4√x + 17
The function is defined as a mathematics expression that defines a relationship between one variable and another variable.
Given the system of functions as
f(x) = √x +4,
And g(x) = x² + 1
To determine the values of f(g(x)) and g(f(x)).
f(g(x)) = g(x) of f(x)
⇒ f(x) = √x +4,
Substiute the values of g(x) in the f(x)
⇒ f(g(x)) = √(x² + 1) +4
g(f(x)) = f(x) of g(x)
⇒ g(x) = x² + 1
Substiute the values of f(x) in the g(x)
⇒ g(f(x)) = (√x +4)² + 1
⇒ g(f(x)) = (√x)² +4² + 4√x + 1
⇒ g(f(x)) = x² + 4√x + 17
Hence, the pair of functions are f(g(x)) = √(x² + 1) +4 and g(f(x)) = x² + 4√x + 17
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