This is because it says "Each triangle has <u>1 obtuse angle</u> and 2 acute angles" in the instructions. An obtuse angle is any angle between 90 and 180 degrees, excluding both endpoints.

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2 years ago

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:

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

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

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

$f(2) + g(-2) = 6$

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 $g(x) = x^2 + 2x +1$ .

(f+g)(x) is the functions f and g added together with 2 substituted for x.

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

(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.

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