Question

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

Answer 1

x^(-5)+4x+1

given f(x)=4x+1 and g(x)=x^(-5)

Explanation:

f(x)=4x+1

g(x)=x^(-5)

(f+g)(x) means you are just going to do f(x)+g(x)

or (4x+1)+(x^(-5))

There are absolutely no like terms so it can't be simplified. We can use commutative and associative property to rearrange the expression.

x^(-5)+4x+1

Answer 2

`(f + g)(x) = \frac{4{x}^(6) \: + {x}^(5) + 1 }{ {x}^(5) }`

EXPLANATION

The given functions are:

`f(x) = 4x + 1`

and

`g(x) = {x}^( - 5)`

We now want to find

`(f + g)(x)`

We use this property of Algebraic functions.

`(f + g)(x) = f(x) + g(x)`

We substitute the functions to get:

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

Writing as a positive index, we get:

`(f + g)(x) = 4x + 1 + \frac{1}{ {x}^(5) }`

The property we used to obtain the positive index is

`{a}^( - n) = \frac{1}{ {a}^(n)}`

We now collect LCD to get:

`(f + g)(x) = \frac{4x \cdot {x}^(5) \: + {x}^(5) + 1 }{ {x}^(5) }`

This simplifies to:

`(f + g)(x) = \frac{4{x}^(6) \: + {x}^(5) + 1 }{ {x}^(5) }`