The one-to-one functions g and hare defined as follows.
g={ (-7,-4), (-2,-9), (3,2), (8,-1) }
h(x)= 4x +9
Find the following:
g^-1 (2)=
h^-1 (x)=
(h o h^-1) (-7) =
To find the inverse of a function g, you need to swap the x and y values of each pair in the function and solve for y.
1. g = { (-7,-4), (-2,-9), (3,2), (8,-1) }
To find g^-1(2), we need to find an x value where the function g outputs 2. Looking at the values in the function g, we see that g(3) = 2. Therefore, the inverse of g, g^-1(2) = 3.
2. h(x) = 4x + 9
To find h^-1(x), we need to swap the x and y values in the function and solve for y.
x = 4y + 9
To solve for y, we isolate it:
x - 9 = 4y
(your can divide it by four to solve with ease)
x - 9 / 4 = y
Therefore, the inverse of h, h^-1(x) = (x - 9) / 4.
3. (h o h^-1)(-7)
To calculate (h o h^-1)(-7), we first find h^-1 of -7 and then evaluate h using that result.
Using the inverse of h, we have h^-1(-7) = (-7 - 9) / 4 = -16 / 4 = -4.
Now we substitute this value into h: h(-4) = 4(-4) + 9 = -16 + 9 = -7.
Therefore, (h o h^-1)(-7) = -7.