Question

For f(x)=4x+1 and g(x)=x^2-5, find (f-g)(x).

Answer 1

C

Explanation:

note (f - g)(x) = f(x) - g(x)

f(x) - g(x)

= 4x + 1 - (x² - 5) ← distribute by - 1

= 4x + 1 - x² + 5 ← collect like terms

= - x² + 4x + 6 ← in standard form → C

Answer 2

For this case we have the following functions:

`f (x) = 4x + 1\\g (x) = x ^ 2-5`

We must find
`(f-g) (x).` By definition we have to:

`(f-g) (x) = f (x) -g (x)`

So:

`(f-g) (x) = 4x + 1- (x ^ 2-5)`

We take into account that:

`- * + = -\\- * - = +\\(f-g) (x) = 4x + 1-x ^ 2 + 5\\(f-g) (x) = - x ^ 2 + 4x + 6`

Answer:

`(f-g) (x) = - x ^ 2 + 4x + 6`

Option C