robert7248
contestada

For [tex]f(x) = 3x + 1[/tex] and [tex]g(x) = x^{2} - 6[/tex], find [tex](f * g)(x)[/tex]

A. [tex]3x^{2} - 17[/tex]
B. [tex]3x^{3} + x^{2} - 6x -6[/tex]
C. [tex]4x^{2} -6x - 8[/tex]
D. [tex]3x^{3} + x^{2} - 18x -6[/tex]

Respuesta :

Answer:

[tex]3x^3+x^2-18x-6[/tex]

Step-by-step explanation:

f(x)= 3x+1 and g(x)= x^2 - 6

we need to find (f*g)(x)

(f*g)(x)= f(x) * g(x)

Plug in the given f(x) and g(x)

[tex](f*g)(x)= f(x) * g(x)= (3x+1)(x^2-6)[/tex]

Apply FOIL method to multiply it

[tex](3x+1)(x^2-6)= 3x^3 -18x+x^2-6= 3x^3+x^2-18x-6[/tex]