contestada

What is (f−g)(x)?

f(x)=5x4+4x3+3x2+2x+1

g(x)=x4+2x3+3x2+4x+5

Enter your answer, in standard form, in the box.


(f−g)(x)=

Respuesta :

19allenethm

Answer:

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

Step-by-step explanation:

To do this, we simply need to subtract the two functions

[tex](5x^4+3x^3+3x^2+2x+1)-(x^4+2x^3+3x^2+4x+5)\\\\5x^4+4x^3+3x^2+2x+1-x^4-2x^3-3x^2-4x-5[/tex]

Now that the negative is distributed, we can combine like terms

[tex]5x^4+4x^3+3x^2+2x+1-x^4-2x^3-3x^2-4x-5\\\\4x^4+2x^3-2x-4[/tex]

This means that our answer is

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

anuksha0456

(f-g)(x) = 4x⁴ + 2x³ - 2x - 4.

What is the functions arithmetic?

Functions arithmetic is similar to algebraic arithmetic. It is just that the whole functions are taken up as variables.

How do we solve the given problem?

We are given that

f(x) = 5x⁴ + 4x³ + 3x² + 2x + 1,

g(x) = x⁴ + 2x³ + 3x² + 4x + 5.

We are asked to find (f-g)(x).

Now, as said in the above definition of functions arithmetic, we get that,

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

or (f-g)(x) = (5x⁴ + 4x³ + 3x² + 2x + 1) - (x⁴ + 2x³ + 3x² + 4x + 5)

On opening the brackets on right side we get,

(f-g)(x) = 5x⁴ + 4x³ + 3x² + 2x + 1 - x⁴ - 2x³ - 3x² - 4x - 5

Now we combine the like terms, to get

(f-g)(x) = (5-1)x⁴ + (4-2)x³ + (3-3)x² + (2-4)x + (1-5)

or, (f-g)(x) = 4x⁴ + 2x³ - 2x - 4

∴  (f-g)(x) = 4x⁴ + 2x³ - 2x - 4

Learn more about Functions Arithmetic at

https://brainly.com/question/13723854

#SPJ2

Otras preguntas