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Find (f . g)(2) for the following functions.f(x) = x^3+ 4 and g(x) = x^2- 1

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Explanation:

is this truly a multiplication of the 2 functions :

(f×g)(x) or (f.g)(x)

or is this a mistyped function of function (composition of functions) :

(f○g)(x) or f(g(x))

if it is truly a multiplication, things are easy.

a mathematical operation between 2 functions just means we do this mathematical person in the functional expressions :

(f×g)(x) = (x³ + 4)×(x² - 1) = x⁵ - x³ + 4x² - 4

for x = 2 we get then

(f×g)(2) = 2⁵ - 2³ + 4×2² - 4 = 32 - 8 + 16 - 4 = 36

if it is a composition of functions after all :

(f○g)(x) = (x² - 1)³ + 4

as we use g(x) as input for f(x) and put the function expression of g(x) into every place of x in f(x).

for x = 2 we get then

(f○g)(2) = (2² - 1)³ + 4 = (4 - 1)³ + 4 =

= 3³ + 4 = 27 + 4 = 31

User Raye
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