Value of the composite function: (f o g)(4) = - 1/2
Step-by-step explanation:
The following notation
(f o g)(x)
Indicates a composite function, and it can be rewritten as
(f o g)(x) = f(g(x))
which can be calculated by using the output of g(x) as input for f(x).
In this problem, the two functions are:
[tex]f(x)=\sqrt{x}-2\\g(x)=\frac{9}{x}[/tex]
We want to calculate (f o g)(4), which means f(g(4)). Therefore, first we calculate g(4):
[tex]g(4)=\frac{9}{4}[/tex]
And then we use this as input for f(x), and we find:
[tex]f(g(4))=\sqrt{g(4)}=\sqrt{\frac{9}{4}}-2=\frac{3}{2}-2=-\frac{1}{2}[/tex]
Learn more about composite functions:
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