Question

Let ​ f(x)=−8x to the 4 power +8x to the 2power −8​ and g(x)=−8x to the 3 power −x​​. a)

Answer 1

`\sf f(x)+g(x) = -8x^4 - 8x^3 + 8x^2 - x-8`

`\sf f(x)-g(x) = -8x^4 +8x^3 + 8x^2 + x-8`

Explanation:

Given:

f(x)=-8x^4+8x^2-8

g(x)=-8x^3 -x

a.

In order to evaluate the sum f(x) + g(x), we simply add the two functions together.

`\begin{aligned} \sf f(x) + g(x) &\sf =( -8x^4 + 8x^2 - 8) +(-8x^3 - x)\\\\&= -8x^4+8x^2 -8-8x^3-x\\\\&\sf = -8x^4 - 8x^3 + 8x^2 - x-8 \end{aligned}`

b.

In order to evaluate the difference f(x) - g(x), we simply subtract the two functions together.

`\begin{aligned} \sf f(x) - g(x) &\sf =( -8x^4 + 8x^2 - 8) -(-8x^3 - x)\\\\&= -8x^4+8x^2 -8+8x^3+x\\\\&\sf = -8x^4 +8x^3 + 8x^2 +x-8 \end{aligned}`

Therefore;

`\sf f(x)+g(x) = -8x^4 - 8x^3 + 8x^2 - x-8`

`\sf f(x)-g(x) = -8x^4 +8x^3 + 8x^2 + x-8`