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Based on the graph below, what is the solution to the equation f(x) = g(x)?


graph of function f of x equals negative x plus 2.5 and graph of function g of x equals x squared plus 2 multiplied by x minus 8

Verified Answer :

Edufirst

The wording of the second function may be interpreted in several differente ways. These are some:

g(x) = (x^2 +2)(x-8)
g(x)=x^2 + 2(x-8)
g(x) x^2 +2x - 8

I will work with the last one, so my system of equation is:

f(x) = - x +2.5
g(x) = x^2 + 2x - 8

f(x) = g(x) ⇒ - x + 2.5 = x^2 + 2x - 8

x^2 + 3x - 8 - x - 2.5 = 0

x^2 + 3x - 10.5 = 0

Use the quadratic formula to solve for x:

x = [ - 3 +/- √(3^2) - 4(1)(-10.5) ]/2

x = - 5.07 and x = 2.07


The solution of the equation f(x) = g(x) are x = 3.055 or x = -6.055 if the f(x) = -x + 2.5 and g(x) = x² +2(x - 8)

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

f(x) = -x + 2.5

g(x) = x² +2(x - 8)

f(x) = g(x)

-x + 2.5 = x² +2(x - 8)

After simplification:

x² + 3x - 18.5 = 0

After solving, we get:

x = 3.055  or  x = -6.055

Thus, the solution of the equation f(x) = g(x) are x = 3.055 or x = -6.055 if the f(x) = -x + 2.5 and g(x) = x² +2(x - 8)

Learn more about the function here:

brainly.com/question/5245372

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