Question

If given f(x) = x 4 and g(x) = –2x2 3x – 1, what is (f –

g.(x)?
a. (f –
g.(x) = –2x2 4x – 3
b. (f –
g.(x) = –2x2 – 2x 5
c. (f –
g.(x) = 2x2 2x 5
d. (f –
g.(x) = 2x2 – 2x 5

Answer 1

`2x^2-2x+5`

Explanation:

Given,

`f(x)=x+4`

`g(x)=-2x^2+3x-1`

`(f-g)(x)=f(x)-g(x)` ( Subtraction of two functions )

`=(x+4)-(-2x^2+3x-1)` ( By substituting values )

`=x+4+2x^2-3x+1` ( Distributive property )

`=2x^2-2x+5` ( Combining like terms )

Hence,

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

Option d is correct.

Answer 2

f(x) = x + 4
g(x) = -2x^2 + 3x - 1
(f - g)(x) = f(x) - g(x) = x + 4 - (-2x^2 + 3x - 1) = x + 4 + 2x^2 - 3x + 1 = 2x^2 - 2x + 5