## Example 2 of finding the function f(x) Using the variable substitution method

In this example, we are given the function f(1- sin x) = sin^{2}x, the question ask for f(x). How to find the f(x)? We are using the variable substitution
method. Let the variable t = 1 - sin x, then sin x = 1 - t, sin^{2}x = (1 - t)^{2}. What is the range of t? Since the maximum value of sin x is 1, when
sin x = 1, t = 1 - sin x = 1 - 1 = 0. Since the minimum value of the sin x is -1, when sin x = -1, t = 1 - six x = 1 - (-1) = 1 + 1 = 2. So the range of t is from 0
to 2. Now we substitute 1 - sin x to t, we get the function f(t) = (1 - t)^{2} and its domain is t in the range of [0, 2]. Now change the variable t to x, we get
f(x) = (1 - x)^{2} and its domain is x in the range of [0. 2].