Given the graph of the function g determine the following g1

Given the graph of the function g, determine the following. g^-1(0) = 0 g^-1(1) = 1 g^-1(g(0)) = 0 g(g^-1(9)) = 9 g^-1(g^-1(1)) = 1

Solution

If a number \'c\' is a point on the graph of g(x) such that g(x_o) = c then g^-1 (c) = x_o

This simply means that x_o is the value on the x axis for which g(x) = c

From the graph, we see that g( - 2) = 0

therefore g ^-1 (0) = - 2

Similarly, g ^-1 (1) means the value of x for which g(x) = 1

this happens for x = -1

therefore g ^-1 (1) = - 1

e) g^-1 (1) = - 1

so, g^-1 (g^-1(1) = g ^-1 ( - 1)

this means the value on the x axis for which g(x) = - 1

this happens for x = - 2.2

therefore  g^-1 (g^-1(1) = - 2.2