If f (x) = x3 + 7x2 - x and g (x) = x2 - 3, what is the degree of g (f (x)) ?

2

3

6

8

G (x) = x^2 - 3

f (x) = x^3+7x^2-x

Start with the g (x) function. Replace every x with f (x)

g (x) = x^2 - 3

g (f (x)) = (f (x)) ^2 - 3

Then replace the f (x) on the right side with x^3+7x^2-x

g (f (x)) = (x^3+7x^2-x) ^2 - 3

The highest term inside the parenthesis is x^3. Squaring this leads to (x^3) ^2 = x^ (3*2) = x^6

So the highest exponent found in g (f (x)) is 6, meaning the degree of is 6

Answer: Choice C) 6

Note: There is no need to expand out the expression as we only need the degree