Answer: To find the inverse of a one-to-one function, you need to switch the inputs and outputs of the original function and solve for the new input. For example, if f(x) = y, then f^(-1)(y) = x 1.
Let’s apply this method to your functions g and h.
g = {(-2, 0), (0, 1), (1, 6), (4, -4)}
To find g^(-1)(1), we need to find the input of g that corresponds to an output of 1. This means we need to look for the ordered pair that has 1 as the second element. We can see that (0, 1) is such a pair, so g(0) = 1. Therefore, g^(-1)(1) = 0.
To find g^(-1)(x), we need to find a general formula for the inverse of g. Since g is given by a set of ordered pairs, we can switch the x and y values of each pair to get the inverse. This gives us:
g^(-1) = {(0, -2), (1, 0), (6, 1), (-4, 4)}
h(x) = 8x + 3
To find h^(-1)(x), we need to find a general formula for the inverse of h. Since h is given by an equation, we can switch the x and y variables and solve for y. This gives us:
x = 8y + 3 x - 3 = 8y y = (x - 3)/8
Therefore, h^(-1)(x) = (x - 3)/8.