Calculus- Early Transcendentals, 2021a

2.5. Logarithms 59
Exercises for 2.4
Exercise 2.4.1 Is the function f (x)=|x| one-to-one?
Exercise 2.4.2 If h(x)=e x + x + 1, find h −1 (2).
Exercise 2.4.3 Find a formula for the inverse of the function f (x)= x + 2
x − 2 .
2.5 Logarithms
Recall the three kinds of exponential functions f (x)=a x depending on whether 0 < a < 1, a = 1ora > 1:
So long as a ≠ 1, the function f (x)=a x satisfies the horizontal line test and therefore has an inverse.
We call the inverse of a x the logarithmic function with base a and denote it by log a . In particular,
The cancellation formulas for logs are:
log a x = y ⇐⇒ a y = x.
log a (a x )=x, foreveryx ∈ R,
a log a (x) = x, foreveryx > 0.