Question

If f(x)=4x^2-6 and g(x)=x^2-4x-8,find (f-g)(x)

a.(f-g)(x)=x^2-14
b.(f-g)(x)=5x^2-4x-14
c.(f-g)(x)=3x^2+4x+2
d.(f-g)(x)=3x^2-4x-2

Answer 1

c. Due to c. and the equation above would be equal just in a different arrangement

Answer 2

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

C is correct

Explanation:

Given:
`f(x)=4x^2-6`

`g(x)=x^2-4x-8`

To find : (f-g)(x)

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

`\Rightarrow (4x^2-6)-(x^2-4x-8)`

using Distributive property

`\Rightarrow 4x^2-6-x^2+4x+8`

`\Rightarrow 4x^2-x^2+4x+8-6`

Combine like term

`\Rightarrow 3x^2+4x+2`

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

Hence, The composite function is
`(f-g)(x)=3x^2+4x+2`