Given fx lnx 3 What is the domain of fx What is the range

Given f(x) = ln(x + 3) What is the domain of f(x)? What is the range of f(x)? Find f^-1 (x) What is the domain of f^-1(x)? What is the range of f^-1 (x)? Using f(x + h) - f(x)/h, find the difference quotient of f(x) = x^3 + 3x - 4.

Solution

domain is { x R : x > -3 }

range is R (all real numbers )

domain of f inverse x = range of f(x) = R

range of f inverse of x = domain of f(x) = { x R : x > -3 }