To find the maximum value of the function f(x)=-

x-10

+6, we need to determine the highest possible output value that the function can have.

First, let’s analyze the function f(x)=-

x-10

+6. The function involves the absolute value of (x-10), which means that the expression inside the absolute value will always be positive or zero. Therefore, the absolute value will always be equal to (x-10).

Now, let’s consider the function without the absolute value: g(x) = -(x-10) + 6. We can simplify this to g(x) = -x + 10 + 6 = -x + 16.

To find the maximum value of g(x), we need to determine the highest possible value for x. Since x can take any real value, there is no upper limit for x. Therefore, there is no maximum value for g(x).

However, we need to consider the original function f(x)=-

x-10

+6. The negative sign in front of the absolute value means that the function is reflected about the x-axis. This reflection changes the behavior of the function.

When x < 10, the expression inside the absolute value becomes negative, and the absolute value becomes the opposite of the expression. Therefore, f(x) = -(x-10) + 6 = -x + 10 + 6 = -x + 16.

When x > 10, the expression inside the absolute value becomes positive, and the absolute value remains the same. Therefore, f(x) = -(x-10) + 6 = -x + 10 + 6 = -x + 16.

When x = 10, the expression inside the absolute value becomes zero, and the absolute value becomes zero. Therefore, f(x) = -(x-10) + 6 = -0 + 6 = 6.

So, the maximum value of f(x)=-

x-10

+6 is 6. This occurs when x = 10.