Find the absolute maximum value of the function f of x equals x squared minus 4 for x between 0 and 4 inclusive and equals negative x plus 16 for x greater than 4 .

A) x = 5.4, x = -1

Step-by-step explanation:

Equations: f(x) = x² - x - 12, g(x) = 3.4x - 6.6

If f(x) = g(x)

Substitute: x² - x - 12 = 3.4x - 6.6

Subtract: x² - 4.4x - 5.4 = 0

Two numbers w/ sum of -4.4x and product of -5.4x²: -5.4x and 1x

Substitute: x² - 5.4x + x - 5.4 = 0

Factor: (x - 5.4)(x + 1) = 0

Solve: x = 5.4, x = -1

g(2) = 3

Step-by-step explanation:

g(x) = x² - 1.

Substituting 2 for x in this formula, we get:

g(2) = 2² - 1, or g(2) = 3

g(2) =3

Step-by-step explanation:

g(x) = x^2 -1

Let x=2

g(2) = 2^2 -1

       =4-1

        =3

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Option a) x = −1, 5.4

Step-by-step explanation:

we have

equate f(x) and g(x)

Solve the quadratic equation by graphing

The solutions are x=-1 and x=5.4

see the attached figure

x = −4, 2.5

Step-by-step explanation:

Let's write this problem algebraically

f(x) = x^2 - x - 12

g(x) = -2.5x - 2

We want to find the solutions to the equation f(x)=g(x) so we set them equal to each other

f(x)=g(x)

x^2 - x - 12 = -2.5x - 2

Adding 2.5x and 2 to both sides,

x^2 + 1.5x - 10 = 0

Factoring, we get

(x + 4) (x - 2.5) = 0

So,

x + 4 = 0 ⇒ x = -4

x - 2.5 = 0 ⇒ x = 2.5

x= -1, 5.4

Step-by-step explanation:

f(x) is a quadratic equation and g(x) is a linear equation

To find f(x)= g(x) we need to find the point where the graph  of f(x) and g(x) intersects.

The quadratic equation f(x) and linear equation g(X) intersects at two points

from the graph f(x)= g(x) at x= -1 and x=5.4