Question

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

A.
`-x^(2) + 4x + 6`
B.
`4x^(2) - 19`
C.
`-x^(2) +4x - 4`
D.
`x^(2) - 4x -6`

Answer 1

Choice A is correct anser.

Explanation:

From question statement,we observe that

Two functions are given. We have to find their difference.

f(x) = 4x+1 and g(x) = x²-5

(f-g)(x) = ?

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

(f-g)(x) = (4x+1)-(x²-5)

(f-g)(x) = 4x+1-x²+5

Adding like terms,we get

(f-g)(x) = 4x-x²+6

(f-g)(x) = -x²+4x+6 which is the solution.

Answer 2

`-x^2+4x+6`

Explanation:

f(x)= 4x+1

g(x)= x^2-5

We need to find (f-g)(x)

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

We need to plug in f(x) and g(x)

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

Now simplify it

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

Combine like terms

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

Final answer is

`-x^2+4x+6`