Question

If f(x) = 6x³ + 5x, g(x) = 3x² +5, and h(x) = 9x² - 8, What is the degree of f(g(h(x)))?

a)2
b)3
c)7
d) 12

Answer 1

• f(x)=6x³+5x
• g(x)=3x²+5
• h(x)=9x²-8

Degree of f(x)=3

Degree of g(x)=2

Degree of h(x)=2

Degree of f(g(h(x)))

• 3(2)(2)
• 12

Option D

Answer 2

d) 12

Explanation:

Given functions:

`f(x)=6x^3+5x`

`g(x)=3x^2+5`

`h(x)=9x^2-8`

As we are only interested in the degrees of the function, we can eliminate the coefficients of each variable and the constants:

• 
  `f(x)=x^3+x`

• 
  `g(x)=x^2`

• 
  `h(x)=x^2`

Therefore:

`\begin{aligned}g[h(x)]& =(x^2)^2\\& =x^4\end{aligned}`

`\begin{aligned}f[g[h(x)]] & = (x^4)^3+x^4\\& = x^(12)+x^4\end{aligned}`

Therefore, the degree of f[g[h(x)]] is 12