Question

Hello! I need some help with this homework question, please? The question is posted in the image below. Q16

Answer 1

Question:

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

Step-by-step 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,

`\sin \colon\mleft[-\pi/2,\pi/2\mright]\to\mleft[-1,1\mright]`

is a bijective function with a domain

`\mleft[-\pi/2,\pi/2\mright]`

and range

`\mleft[-1,1\mright].`

Now the inverse sine function i.e.,

`\sin ^(-1)\colon\mleft[-1,1\mright]\to\mleft[-\pi/2,\pi/2\mright]`

has the domain

`\mleft[-1,1\mright]`

equal to the range of the sine function and the range of the function as

`\mleft[-\pi/2,\pi/2\mright]`

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