Answer: 62/5
Explanation:
You are given the following functions:
F(X) = x-2/5
g(X) = x-5
First find the inverse of the two functions.
To find inverse, first make f(x) and g(x) equal to y, interchange x and y and make y the subject of formula
F(x) = x - 2/5
Y = x - 2/5
Interchange y and x
X = y - 2/5
Make y the subject of formula
Y = x + 2/5
Therefore, f^-1(x) = x + 2/5 ..... (1)
Also,
g(x) = x - 5
Y = x - 5
X = y - 5
Make y the subject of formula
Y = x + 5
g^-1(x) = x + 5
To find g inverse of 7, substitute 7 for x in the above formula
g^-1(7) = 7 + 5 = 12
f inverse g inverse = 7 will be achieved by substitute 12 for x in the equation (1)
F^-1(12) = 12 + 2/5 = 62/5