Answer: F^-1(x) is a function.
Step-by-step explanation:
To find the inverse of a function, we need to swap the x and y variables and then solve for y in terms of x. Let’s start by replacing f(x) with y:
y = -3x + 8
Next, we’ll swap the x and y variables:
x = -3y + 8
Now, we’ll solve for y:
x - 8 = -3y
y = (x - 8) / -3
Therefore, the inverse of F(x) = -3x + 8 is:
F^-1(x) = (x - 8) / -3
To determine whether F^-1(x) is a function, we need to check if there are any values of x that produce more than one value of y. In other words, we need to check if F^-1(x) passes the vertical line test. Since F^-1(x) is a straight line with a slope of -1/3, it passes the vertical line test and is therefore a function.
Therefore, F^-1(x) is a function.
