Exponential functions are one-to-one functions. ... The parent function, y = b^x, will always have a y-intercept of one, occurring at the ordered pair of (0,1). Algebraically speaking, when x = 0, we have y = b⁰ which is always equal to 1.

Do exponential functions have an inverse?

Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = a^x is x = a^y. ... It is called the logarithmic function with base a.

Are exponential and log functions one to one?

Considering the natural logarithm, it is the inverse of the exponential function ex:R→(0,∞) , which is strictly monotonically increasing, so ln:(0,∞)→R is itself strictly monotonically increasing and one to one. Any other logarithm is expressible as a constant multiple of ln , so is also one to one.