Question

If f(x) = x3 + 7x2 – x and g(x) = x2 – 3, what is the degree of g(f(x))?
2
3
6
8

Answer 1

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

Answer 2

Answer: C. 6 on edge :)