Which term is the inverse of an exponential function?

Which term is the inverse of an exponential function?

• A. Logarithmic function
• B. Quadratic
• C. Exponential function
• D. Syntax error

Answer: (A)

Inverse functions swap inputs and outputs, so this question is about what undoes exponentiation. If you have an exponential function f(x) = b^x, its inverse is the logarithmic function log_b(y), because taking the logarithm finds the exponent that returns y when you raise the base b to that power. In other words, log_b(b^x) = x and b^{log_b(y)} = y. This shows why the logarithmic function is the inverse of an exponential function, with the natural logarithm ln being the inverse when the base is e. The other options aren’t inverse relationships to exponentiation.

Inverse functions swap inputs and outputs, so this question is about what undoes exponentiation. If you have an exponential function f(x) = b^x, its inverse is the logarithmic function log_b(y), because taking the logarithm finds the exponent that returns y when you raise the base b to that power. In other words, log_b(b^x) = x and b^{log_b(y)} = y. This shows why the logarithmic function is the inverse of an exponential function, with the natural logarithm ln being the inverse when the base is e. The other options aren’t inverse relationships to exponentiation.