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.

Question

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.

Knowee AI · Accepted Answer

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.

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.

Solution

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