Question

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

Answer 1

ANSWER

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

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:

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

Answer 2

Answer:

x^(-5)+4x+1

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

Step-by-step 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