Question

If f(x) = –x3, g(x) = 3x2 – 1, and h(x) = 2x + 5, what is the degree of [f o g o h](x)?

Answer 1

I reckon the degree will be 6

Answer 2

The degree of [f o g o h](x) is 6.

Explanation:

We are given the following information:

`f(x) = -x^3\\g(x) = 3x^2 - 1\\ h(x) = 2x + 5`

we have to find degree of [f o g o h](x)

[f o g o h](x) =

`f \circ g \circ h = f(g(h(x)))`

Putting the values,

`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`

The degree of above expression is 6.

Thus, the degree of [f o g o h](x) is 6.