Question

Given that f(x) = x2 + 6x – 2, g(x) = x – 7, and h(x) = x + 4 find each function.

(g − f)(x)

a) –x2 – 5x – 5

b) x2 + 5x + 5

c) –x2 + 5x + 5

d) x2 – 5x – 5

Answer 1

`(g-f)(x)=-x^2-5x-5`

which agrees with answer a) in the list.

Explanation:

You are asked to find the difference of two functions:
`(g-f)(x)`,

so write both in the order requested (first g(x) and subtract from it f(x)). Then use distributive property to eliminate parentheses, and combine all like terms. Finally, arrange the resulting polynomial in standard form:

`f(x)=x^2+6x-2\\g(x)=x-7\\(g-f)(x)= (x-7)-(x^2+6x-2)\\(g-f)(x)=x-7-x^2-6x+2\\(g-f)(x)=-x^2-5x-5`