The values of the composite functions are (f.g)(x) = 2x^3 - 19x^2 + 40x + 25 and (f/g)(x) = 2x + 1
The functions are given as:
f(x) = 2x^2 - 9x - 5
g(x) = x - 5
The composite function (f.g)(x) is calculated as
(f.g)(x) = f(x) * g(x)
This gives
(f.g)(x) = (2x^2 - 9x - 5) * (x - 5)
Evaluate the product
(f.g)(x) = 2x^3 - 9x^2 - 5x - 10x^2 + 45x + 25
Evaluate the like terms
(f.g)(x) = 2x^3 - 19x^2 + 40x + 25
The composite function (f/g)(x) is calculated as
(f/g)(x) = f(x)/g(x)
This gives
(f/g)(x) = (2x^2 - 9x - 5)/(x - 5)
Factorize the numerator
(f/g)(x) = (2x + 1)(x - 5)/(x - 5)
Evaluate the quotient
(f/g)(x) = 2x + 1
Hence, the values of the composite functions are (f.g)(x) = 2x^3 - 19x^2 + 40x + 25 and (f/g)(x) = 2x + 1
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