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

defazajx

defazajx

Answered question

2021-09-09

Given f(x)=4x23andg(x)=612x2
b. (g of f)(2)

Answer & Explanation

Velsenw

Velsenw

Skilled2021-09-10Added 91 answers

Obtain the composite function (g of f)(x).
The given two functions are f(x)=4x23andg(x)=612x2.
To obtain the composite function (g of f)(x), substitute f(x) for x in the function g(x).
The composite function (g of f)(x) is obtained as 192x4288x2+10732x448x2+18 from the calculation given below:
(gf)(x)=g(f(x))
=g(4x23)
=612(4x23)2
=612(16x4+924x2)
=6×(32x4+1848x2)132x4+1848x2
192x4288x2+10732x448x2+18
Obtain the value of (g of f)(2).
The composite function (g o f)(x) is obtained as 192x4288x2+10732x448x2+18.
To obtain the value of (g of f)(2), substitute 2 in place of x in the composite function (g of f)(x) =192x4288x2+10732x448x2+18.
The value of (g o f)(2) is obtained as 5.997 from the calculation given below:
(gf)(x)=192x4288x2+10732x448x2+18
(gf)(2)=192(2)4

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