Determine if 2 Functions are Inverses by Compositions

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Determine if 2 Functions are Inverses by Compositions

You can use composition of functions to verify that 2 functions are inverses. The inverse functions “undo” each other, When you compose two inverses… the result is the input value of x. If f(g(x)) = g(f(x)) = x Then f(x) and g(x) are inverse functions

Because f(g(x)) = g(f(x)) = x, they are inverses. Example 1: Determine by composition if the functions are inverses functions. Because f(g(x)) = g(f(x)) = x, they are inverses.

Find the composition f(g(x)). Example 2: Determine by composition whether each pair of functions are inverses. 1 3 f(x) = 3x – 1 and g(x) = x + 1 Find the composition f(g(x)). = x + 3 – 1 f(g(x)) = x + 2 The functions are NOT inverses.

Because f(g(x)) = g(f(x)) = x, they are inverses. Example 3 Determine whether are inverse functions. Because f(g(x)) = g(f(x)) = x, they are inverses.

Because f(g(x)) = g(f(x)) = x, they are inverses. Example 4 Determine by composition whether each pair of functions are inverses. 3 2 f(x) = x + 6 and g(x) = x – 9 Find the composition f(g(x)) and g(f(x)). = x – 6 + 6 = x + 9 – 9 Because f(g(x)) = g(f(x)) = x, they are inverses.

Find the compositions f(g(x)) and g(f(x)). Example 5 f(x) = x2 + 5 and for x ≥ 0 Find the compositions f(g(x)) and g(f(x)). Substitute for x in f. = x + 25 +5 10 x - Simplify. Because f(g(x)) ≠ x, f (x) and g(x) are NOT inverses.