In (a)–(d), determine whether f and g are inverse functions.(a) f(x) = 4x, g(x) = 14 x
Question
In (a)–(d), determine whether f and g are inverse functions.(a) f(x) = 4x, g(x) = 14 x
Solution
To determine if two functions are inverses of each other, we need to check if the composition of the two functions in both orders results in the identity function. The identity function is a function that always returns the same value that was used as its argument.
The composition of two functions f and g is denoted as f(g(x)) or g(f(x)).
(a) For f(x) = 4x and g(x) = 14x, let's check:
f(g(x)) = f(14x) = 4 * 14x = 56x g(f(x)) = g(4x) = 14 * 4x = 56x
Neither of these is the identity function (which would be x), so f and g are not inverse functions.
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We use Blank 1 Question 5 to tell if two functions are inverses of each other.
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