Question

If f(c) = -x^3, g(x)= 3x^2-1, and h(x)=2x+5, what is the degree of [f*g*h](x) ??

Answer 1

Choice D is correct answer.

Explanation:

We have given three functions.

f(x) =-x³, g(x) = 3x²-1 and h(x) = 2x+5

We have to find composition of above functions.

(fogoh)(x) = ?

The formula to find composition of functions is:

(fogoh)(x) = f(g(h(x)))

Putting values in above formula, we have

(fogoh)(x) = f(g(2x+5)

(fogoh)(x) = f(3(2x+5)²-1)

(fogoh)(x) = f( 3(4x²+20x+25)-1)

(fogoh)(x) = f(12x²+60x+125-1)

(fogoh)(x) = f( 12x²+60x+124)

(fogoh)(x) = -(12x²+60x+124)³

Hence, degree of polynomial is 6.

Answer 2

Degree of the given expression will be 6.Option 4 is the correct answer.

Explanation:

The given functions are f(x) = -x³, g(x) = 3x²-1, h(x) = 2x+5

and we have to find the value of [fogoh](x).

First we will evaluate (goh)(x) = [3(2x+5)²-1] [By putting h(x) in place of x in g(x)]

(goh)(x) = [3(4x²+25+20x)-1] = 912x²+75+60x-1 = 912x²+60x+74

Now (fogoh)(x) = -(912x²+60x+74)³

Form the expansion of this expression we will get a polynomial of 6 degree.

Therefore Option 4 is the right answer.