Functions of functions are evaluated by taking first's output as second's input. The representation of [tex]f[g(x)][/tex] is: Option D: [tex]f[g(x)] = 2x^2 + 21[/tex]
Functions which are formed by composing two or more functions in a way that one's output is another's input are called composite functions. They are also called function of functions.
The given functions are
Then [tex]f[g(x)][/tex] will be evaluated as output of g(x) taken as input for f(x).
Thus,
[tex]f[g(x)] = 2[g(x)] + 5 = 2[x^2 + 8] + 5\\\\f[g(x)] = 2x^2 + 21[/tex]
[tex]f[g(x)] = 2[g(x)] + 5 = 2[x^2 + 8] + 5\\\\f[g(x)] = 2x^2 + 21[/tex]
Thus,
The representation of [tex]f[g(x)][/tex] is: Option D: [tex]f[g(x)] = 2x^2 + 21[/tex]
Learn more about composite functions here:
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