Which is the identity function?

Which is the identity function?

• A. f(x) = x.
• B. f(x) = x^2.
• C. f(x) = 0.
• D. f(x) = ln x.

Answer: (A)

An identity function is one that returns its input unchanged: f(x) = x for every x in its domain. That property means when you plug in any number, you get the same number back. The expression f(x) = x exactly does that, so it is the identity function. The other expressions don’t work as the identity. f(x) = x^2 sends 3 to 9 (and even negative numbers to positive values), so it doesn’t always return x. f(x) = 0 maps every input to 0, which is not equal to x except at x = 0. f(x) = ln x is only defined for x > 0 and equals x only at x = 1, not for all x in its domain.

An identity function is one that returns its input unchanged: f(x) = x for every x in its domain. That property means when you plug in any number, you get the same number back. The expression f(x) = x exactly does that, so it is the identity function.

The other expressions don’t work as the identity. f(x) = x^2 sends 3 to 9 (and even negative numbers to positive values), so it doesn’t always return x. f(x) = 0 maps every input to 0, which is not equal to x except at x = 0. f(x) = ln x is only defined for x > 0 and equals x only at x = 1, not for all x in its domain.