Question

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

Answer 1

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

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.

Answer 2

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.