Mathematics: f(x) = 2x3 + 3x2 - 7x + 2 g(x) = 2x - 5 Find ( f+ g)(x).

Mathematics : asked on Cartucho1978

11.04.2023

f(x) = 2x3 + 3x2 - 7x + 2
g(x) = 2x - 5
Find ( f+ g)(x).

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Faq

Mathematics

Use the functions f(x)=7x3−3x2−x+14 f x = 7 x 3 - 3 x 2 - x + 14 and g(x)=2x3+2x+5 g x = 2 x 3 + 2 x + 5 as examples to show that the set of polynomials is closed under subtraction.

Step-by-step answer

P Answered by PhD

The given set of polynomials f(x) and g(x) are closed under subtraction.

Step-by-step explanation:

Given that the functions f ad g are defined by

f(x)=7x^3-3x^2-x+14 and g(x)=2x^3+2x+5 respectively.

To show that the set of polynomials is closed under subtraction :

Now subtract the given polynomials

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

=7x^3-3x^2-x+14-(2x^3+2x+5)

=7x^3-3x^2-x+14-2x^3-2x-5

=5x^3-3x^2-3x+9

∴ f(x)-g(x)=5x^3-3x^2-3x+9

When subtracting the polynomials the variables and their exponents remains same only variation in their coefficients.Hence the given polynomials f(x) and g(x) are closed under subtraction.

∴ f(x)-g(x)=5x^3-3x^2-3x+9 are closed under subtraction,

Hence showed.

Mathematics

Use the functions f(x)=7x3−3x2−x+14 f x = 7 x 3 - 3 x 2 - x + 14 and g(x)=2x3+2x+5 g x = 2 x 3 + 2 x + 5 as examples to show that the set of polynomials is closed under subtraction.

Step-by-step answer

P Answered by PhD

The given set of polynomials f(x) and g(x) are closed under subtraction.

Step-by-step explanation:

Given that the functions f ad g are defined by

f(x)=7x^3-3x^2-x+14 and g(x)=2x^3+2x+5 respectively.

To show that the set of polynomials is closed under subtraction :

Now subtract the given polynomials

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

=7x^3-3x^2-x+14-(2x^3+2x+5)

=7x^3-3x^2-x+14-2x^3-2x-5

=5x^3-3x^2-3x+9

∴ f(x)-g(x)=5x^3-3x^2-3x+9

When subtracting the polynomials the variables and their exponents remains same only variation in their coefficients.Hence the given polynomials f(x) and g(x) are closed under subtraction.

∴ f(x)-g(x)=5x^3-3x^2-3x+9 are closed under subtraction,

Hence showed.

Mathematics

An ice cream shop offers 5 different flavors of ice cream and 9 different toppings. How many choices are possible for a single serving of ice cream with one topping?

Step-by-step answer

P Answered by PhD

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45

Mathematics

A new school randomly assigns a six-character student code to every prospective student. The school uses the characters 1, 2, 3, 4, 5, X, Y, and Z. If none of the student codes contain a repeated character, what is the total number of codes that can be randomly assigned?