Given f(x) = 4x^(2)-3 and g(x) = 6 - frac(1)(2)x^2 a. (f of g)(4)

avissidep

avissidep

Answered question

2021-09-12

Given f(x)=4x23andg(x)=612x2
a. (f of g)(4)

Answer & Explanation

Arnold Odonnell

Arnold Odonnell

Skilled2021-09-13Added 109 answers

Composite function:
A composite function is a function that depends on another function. This composite function is created by substituting one function into another function.
f(g(x)) is a composite function which is formed by substituting g(x) for x in f(x). The composite function f(g(x)) is also written as (f of g)(x) or fg(x). This can be read as “f of g of x".
The given two functions are f(x)=4x23andg(x)=612x2
To obtain the composite function (f o g)(x), substitute g(x) for x in the function f (x).
The composite function (f o g)(x) is obtained as 14124x2+1x4 from the calculation given below:
(fg)(x)=f(g(x))
=fbigg(612x2bigg)
=4×bigg(612x2bigg)23
=4×bigg(366x2+14x4bigg)3
=14424x2+1x43
=14124x2+1x4
Obtain the value of (f of g)(4).
The composite function (f of g)(x)is obtained as =14124x2+1x4
To obtain the value of (f o g)(4), substitute 4 in place of x in the composite function (f of g)(x) =14124x2+1x4
The value of (f o g)(4) is obtained as 139.5039 from the calculation given below: (fg)(x)=14124x2+1x4
(fg)(4)=1412442+144
=1411.5+0.0039
139.5039

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