Answer:
Question:
If f and g are inverse functions, the domain of f is the same as the range of g.
Explanation:
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 a range of A) and range is A (which is the domain of f).
For example The trigonometric sine function,
[tex]\sin \colon\mleft[-\pi/2,\pi/2\mright]\to\mleft[-1,1\mright][/tex]
is a bijective function with a domain
[tex]\mleft[-\pi/2,\pi/2\mright][/tex]
and range
[tex]\mleft[-1,1\mright].[/tex]
Now the inverse sine function i.e.,
[tex]\sin ^{-1}\colon\mleft[-1,1\mright]\to\mleft[-\pi/2,\pi/2\mright][/tex]
has the domain
[tex]\mleft[-1,1\mright][/tex]
equal to the range of the sine function and the range of the function as
[tex]\mleft[-\pi/2,\pi/2\mright][/tex]
equal to the domain of the sine function.
Therefore,
Therefore, the statement if f and g are inverse functions, the domain of f is the same as the range of g isTRUE
