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Example 1 of finding the function f(x) Using the variable substitution method

In this example, we are given the function f(2x + 3) = 5x + 2, the question ask for f(x). How to find the f(x)? We are using the variable substitution method. Let the variable t = 2x + 3, then 2x = t - 3, x = (t - 3)/2. Now substitute the variable t to the given function. f(t) = 5 × (t - 3)/2 + 2 = (5t - 15)/2 + 2 = (5/2)t - 15/2 + 4/2 = (5/2)t - 11/2. Now change the variable t to x, we get the function f(x) = (5/2)t - 11/2.