Question

The domain for f(x) and g(x) is all real numbers. Let f(x) = 3x^2 + x-7 and g(x) = x^2 + 4x-5

Find (f-g)(x).

SHOW WORK PLEASE

Answer 1

`(f-g)(x) =  2x^(2)  - 3x -2`

Explanation:

Here, the given functions are:

`f(x) = 3x^(2)  + x -7\\g(x) = x^(2) + 4x - 5`

Now, as both the functions are POLYNOMIAL, and POLYNOMIAL FUNCTION FOLLOW THE LINEAR TRANSFORMATION.

⇒(f-g)(x) = f(x) - g(x)

Now ,
`f(x) - g(x)  = 3x^(2)  + x -7 -(x^(2) + 4x - 5)\\   =  3x^(2)  + x -7 - x^(2)  - 4x+5`

=
`(3x^(2)  - x^(2))  + (x  - 4x)  -7  +5  = 2x^(2)  - 3x -2`

`\implies f(x) - g(x) =  2x^(2)  - 3x -2`

Or,
`(f-g)(x) =  2x^(2)  - 3x -2`