[tex]\text{The value of } (f.g)(x) \text{ is }(f \times g)(x) =x^3-3x^2+2x-6[/tex]
Solution:
Given that:
[tex]f(x) = x^2+2[/tex]
[tex]g(x) = x - 3[/tex]
We have to find (f . g)(x)
The formula for (f . g)(x) is given as:
[tex](f \times g)(x) = (f (x))(g(x))[/tex]
Substitute the given functions f(x) and g(x)
[tex](f \times g)(x) =(x^2+2)(x-3)[/tex]
Multiply both functions
Multiply each term in first bracket with each terms in second bracket
[tex](f \times g)(x) = (x^2)(x)-3(x^2)+2(x) + 2(-3)\\\\(f \times g)(x) =x^3-3x^2+2x-6[/tex]
Thus the value of (f .g)(x) is found
