True or False. If f and g are inverse functions, the domain of f is the same as the range of g.

Solution:

If f: A → B is a bijective function, then the inverse function of f, say g will be a function such that g: B → A whose domain is B (which is range of A) and range is A (which is domain of f).

For example: The trigonometric sine function, sin: [-π/2, π/2] → [-1, 1] is a bijective function with a domain [- π/2, π/2] and range [-1, 1].

Now the inverse sine function i.e., sin^-1:[-1, 1] → [-π/2, π/2] has the domain [-1, 1] equal to the range of the sine function and the range of the function as [-π/2, π/2] equal to the domain of the sine function.

Therefore, the statement if f and g are inverse functions, the domain of f is the same as the range of g is true.

True or False. If f and g are inverse functions, the domain of f is the same as the range of g.

Summary:

The statement if f and g are inverse functions, the domain of f is the same as the range of g is true.