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Sagot :
- 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:
d) 12
Step-by-step explanation:
Given functions:
[tex]f(x)=6x^3+5x[/tex]
[tex]g(x)=3x^2+5[/tex]
[tex]h(x)=9x^2-8[/tex]
As we are only interested in the degrees of the function, we can eliminate the coefficients of each variable and the constants:
- [tex]f(x)=x^3+x[/tex]
- [tex]g(x)=x^2[/tex]
- [tex]h(x)=x^2[/tex]
Therefore:
[tex]\begin{aligned}g[h(x)]& =(x^2)^2\\& =x^4\end{aligned}[/tex]
[tex]\begin{aligned}f[g[h(x)]] & = (x^4)^3+x^4\\& = x^{12}+x^4\end{aligned}[/tex]
Therefore, the degree of f[g[h(x)]] is 12
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