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Jobisdone [24]
2 years ago
10

Let f(x) = 8x3 + 16x2 − 15 and g(x) = 2x + 1. Find f of x over g of x.

Mathematics
1 answer:
andrey2020 [161]2 years ago
3 0

Answer:

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Let f(x)=x²+kx+4 and g(x)=x³+x²+kx+2k, where k is a real constant.
antoniya [11.8K]

The value of k such that the graph of f and the graph of g only intersect one is equal to 2.

The value of k such that the graph of f and the graph of g only intersect one is equal to 2. According to the image attached below, functions f(x) and g(x) intersect at point (x, y) = (0, 4) for k = 2.

<h3>How to find the value of the constant k of a system of two polynomic equations</h3>

Herein we have a system formed by two <em>nonlinear</em> equations, a <em>quadratic</em> equation and a <em>cubic</em> equation. Given the constraint that both function must only intersect once, we have the following expression:

f(x) - x² - k · x = 4       (1)

g(x) - x² - k · x = x³ + 2 · k        (2)

x³ + 2 · k = 4

x³ + 2 · (k - 2) = 0

If f and g must intersect once, then the roots must of the form:

(x - r)³ = x³ + 2 · (k - 2)

x³ - 3 · r · x² + 3 · r² · x - r³ = x³ + 2 · (k - 2)

Then, the following conditions must be met: - 3 · r · x² = 0, 3 · r² · x = 0. If x may be any real number, then r must be zero and the value of k must be:

2 · (k - 2) = 0

k - 2 = 0

k = 2

Therefore, the value of k such that the graph of f and the graph of g only intersect one is equal to 2. According to the image attached below, functions f(x) and g(x) intersect at point (x, y) = (0, 4) for k = 2.

To learn more on polynomic functions: brainly.com/question/24252137

#SPJ1

7 0
1 year ago
-5 and 1 which is greater in value
mash [69]

Answer:

1 is greater than -5

Step-by-step explanation:

1 is greater than -5 because 1 is a whole number while -5 is a number that isn't positive causing it to automatically be lower then 1.

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loris [4]

Answer:

Step-by-step explanation:

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2 years ago
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There is a difference between A and a

Step-by-step explanation:

When you are labeling angles, capitol letter means the angle degree while a lowercase letter means a side length.

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2 years ago
Use coordinate notation to describe the translation
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