Question

For align="absmiddle" class="latex-formula"> and $g(x) = x^{2} - 6$, find $(f * g)(x)$
A. $3x^{2} - 17$
B. $3x^{3} + x^{2} - 6x -6$
C. $4x^{2} -6x - 8$
D. $3x^{3} + x^{2} - 18x -6$

Answer 1

Answer:

$3x^3+x^2-18x-6$

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)

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

Apply FOIL method to multiply it

$(3x+1)(x^2-6)= 3x^3 -18x+x^2-6= 3x^3+x^2-18x-6$