if (f(x)=3x^{2}) and (g(x)=4x^{3}+1), what is the degree of ((fcirc g)(x))?\n2\n3\n5\n6

Explanation:

Step1: Recall composition formula

$(f\circ g)(x)=f(g(x))$.

Step2: Substitute $g(x)$ into $f(x)$

Given $f(x) = 3x^{2}$ and $g(x)=4x^{3}+1$, then $f(g(x))=3(4x^{3}+1)^{2}$.

Step3: Expand $(4x^{3}+1)^{2}$ using $(a + b)^{2}=a^{2}+2ab + b^{2}$

$(4x^{3}+1)^{2}=(4x^{3})^{2}+2\times4x^{3}\times1 + 1^{2}=16x^{6}+8x^{3}+1$.

Step4: Multiply by 3

$f(g(x))=3(16x^{6}+8x^{3}+1)=48x^{6}+24x^{3}+3$.

Answer:

6