Question

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

Answer 1

I hope this helps you

Answer 2

Keywords:

Functions, subtraction, operation of functions

For this case, we are given two functions of the form
`y_ {1} = f (x)`, where
`f (x) = 4x + 1` and
`y_ {2} = g (x)`, where
`g (x) = x ^ 2-5`. We must find the subtraction (f-g) (x). So, by definition of operation of functions we have to:

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

So, we have:

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

Knowing that:
`- * + = -\ and\ - * - = +`

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

Answer:

`(f-g) (x)`is given by
`-x ^ 2 + 4x + 6`