Question

if f(x)=3x^2 and g(x)=4x^3=1, what is the degree of (fog)(x)

Answer 1

f(x) = 3x^2

g(x) = 4x^3 + 1

(fog)(x) = 3(4x^3 +1)^2

= 48x^6 + 24x^3 + 3

The degree is the highest exponent on the variable, which is 6.

Answer 2

Answer: The degree of (fog)(x) =6

Step-by-step explanation:

Given:

       $f(x)=3 x^{2}$

       $g(x)=4 x^{3}+1$

To find:

     The degree of (fog) (x)

Solution:

Formula used for calculating fog (x) is given as:

(fog) (x)=[f(g(x))]

Substitute the value of f(x) and g(x) in the above equation, we get

    (fog) (x)=$3\left(4 x^{3}+1\right)^{2}$

                =$3\left[16 x^{6}+2\left(4 x^{3}+1\right)+1\right]$                      

                =$3\left[16 x^{6}+8 x^{3}+2+1\right]$

                =$48 x^{6}+24 x^{3}+6+3$  

                =$48 x^{6}+24 x^{3}+9$

(fog) (x)=$48 x^{6}+24 x^{3}+9$

Result:

The degree of (fog) (x)=$48 x^{6}+24 x^{3}+9$ is Six.