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2 years ago

Given the function, g(x)=5x^5/x^3-2x+1, choose the correct horizontal asymptote. none y = 0 y = 1 y = 3

Mathematics

1 answer:

viktelen [127]2 years ago

8 0

Answer: NONE

<u>Step-by-step explanation:</u>

Consider that m is the degree of the numerator and n is the degree of the denominator.

The rules for horizontal asymptote (H.A.) are as follows:

If m > n then no H.A. (use long division to find the slant asymptote)

If m = n then H.A. is y = leading coefficient of numerator/leading coefficient of denominator

If m < n then H.A. is y = 0

Given: g(x) = 5x⁵/(x³ - 2x + 1)

--> m = 5, n = 3

Since m > n then there is no H.A.

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Given that f(x)= 2x+1 and g(x)= x^2 +2x+1 find (F+g)(2). Find (F.g)(x) find f(x)/g find f(2) +g(-2)?

Pepsi [2]

Answer:

$(f+g)(2) = 14$

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

$\frac{f(x)}{g(x)} = \frac{2x+1}{x^2+2x+1}$

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Step-by-step explanation:

Function composition and transformation combines functions together using operations such as addition, subtraction, multiplication, division and substitution. To find each, perform the operation with the functions f(x) = 2x+1 and $g(x) = x^2 + 2x +1$ .

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$(f+g)(x) = 2x+1 + x^2 +2x + 1 = x^2 + 4x + 2\\(f+g)(2) = 2^2 + 4(2) + 2 = 14$

(f·g)(x) is function composition that means f(g(x)) or substitute g(x) into f(x).

$f(g(x)) = 2(x^2+2x+1)+1 = 2x^2 + 4x+2 + 1\\f(g(x)) = 2x^2 + 4x +3$

f(x) / g(x) is division of the two functions. Division can only occur with polynomials if they share the same factors or things which multiply to create them. If none are present, do not simplify.

$\frac{f(x)}{g(x)} = \frac{2x+1}{x^2+2x+1}$

This cannot be simplified.

f(2) + g(-2) means find the function value of f at 2 and the function value of g at -2 then add them together.

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

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