Answer:
The degree of [f o g o h](x) is 6.
Step-by-step explanation:
We are given the following information:
[tex]f(x) = -x^3\\g(x) = 3x^2 - 1\\ h(x) = 2x + 5[/tex]
we have to find degree of [f o g o h](x)
[f o g o h](x) =
[tex]f \circ g \circ h = f(g(h(x)))[/tex]
Putting the values,
[tex]f(g(h(x)))\\\\=f(g(2x + 5)\\\\= f(3(2x+5)^2-1)\\\\= -(3(2x+5)^2-1)^3\\\\= -(3(4x^2+25+20x)-1)^3\\\\=-(12x^2+60x+74)^3\\\\= -1728x^6-25920x^5-161568x^4-535680x^3-996336x^2-985680x-405224[/tex]
The degree of above expression is 6.
Thus, the degree of [f o g o h](x) is 6.
