Question

Let f(x)=−|x−4|+4 and g(x)=1/2x−4. Graph the functions in the same coordinate plane. What are the solutions to f(x)=g(x)? Enter your answers in the boxes from smallest to largest.

x =
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Answer 1

Explanation:

To find the solutions to f(x) = g(x), we need to find the values of x that make the two sides of the equation equal.The function f(x) = −|x−4| + 4 is a piecewise function. For x≤4, f(x) = −(x−4) + 4 = 4−x and for x>4, f(x) = (x−4) + 4 = x.The function g(x) = 1/2x − 4 is a linear function.When we graph these two functions in the same coordinate plane, we can see that they intersect at the point (4, 4) this point is the only solution where f(x) = g(x)so the solution of x = 4

x = 4