Question

If f(x)=6x^3+5x,g(x)=3x^2+5,and h(x)=9x^2-8 what is the degree of f(g(h(x))) awer choices are a.2 b.3 3.7 4.12

Answer 1

The degree is 12

Explanation:

Answer 2

To find f(g(h(x))), we need to find g(h(x)) first. To do that we are going to evaluate the function g(x) at h(x):
We know that
`h(x)=9x^2-8` and
`g(x)=3x^2+5`

`g(h(x))=g(9x^2-8)=3(9x^2-8)^2+5`

`=3(81x^4-144x^2+64)+5`

`=243x^4-432x^2+192+5`

`=243x^4-432x^2+197`

Now that we know that
`g(h(x))=243x^4-432x^2+197`, to find
`f(g(h(x)))` we are going to evaluate
`f` at
`243x^4-432x^2+197`

`f(g(h(x)))=f(243x^4-432x^2+197)`

`f(243x^4-432x^2+197)=6(243x^4-432x^2+197)^3`
`+5(243x^4-432x^2+197)`


`=86093442x^(12)-459165024x^(10)+1025681130x^8-1228219200x^6`
`+83152048x^4-301780944x^2+45873223`

Since the degree of a polynomial is the highest degree of its monomials, we can conclude that the degree of f(g(h(x))) is 12