Question

Let f(x) =-7x^(4)-5x^(2)+2 and g(x)= 7x^(3)+x

a) Evaluate the sum f(x) +g(x)
b) Evaluate the difference f(x)-g(x)

Answer 1

a) To evaluate the sum f(x) + g(x), you simply add the two functions together:

f(x) + g(x) = (-7x^4 - 5x^2 + 2) + (7x^3 + x)

Simplify the terms:

f(x) + g(x) = -7x^4 + 7x^3 - 5x^2 + x + 2

b) To evaluate the difference f(x) - g(x), subtract the second function from the first:

f(x) - g(x) = (-7x^4 - 5x^2 + 2) - (7x^3 + x)

Simplify the terms:

f(x) - g(x) = -7x^4 - 7x^3 - 5x^2 - x + 2

These are the expressions for the sum and difference of the two functions f(x) and g(x).

Answer 2

Explanation:

(-7x⁴ - 5x² + 2) + (7x³ + x)

-7x⁴ - 5x² + 2 + 7x³ + x

-7x⁴ + 7x³ - 5x² + x + 2

b) (-7x⁴ - 5x² + 2) - (7x³ + x)

-7x⁴ - 5x² + 2 - 7x³ - x

-7x⁴ - 7x³ - 5x² - x + 2