Question

TRUE/FALSE

Let f(x)= tan^-1(x). Then the domain would be (0,pi) and the range is all real numbers.

Answer 1

i think the domain would be all real numbers

Answer 2

@ganeshie8

Answer 3

its false

Answer 4

tanx is one-to-one and onto in (-pi/2, pi/2)

Answer 5

so thats the principal domain for tanx if we wanto think of its inverse

Answer 6

within that range, tanx outputs all real numbers
so the domain of its inverse wud be all real numbers as well

Answer 7

so domain of tan^-1(x) is all real numbers

Answer 8

Thank you everyone!!!

Answer 9

does that make some sense ha ?

Answer 10

Yep!

Answer 11

The domain of a function, f(x) is the set of all the allowed values of x (the input to f);
the range is the set of values of f (the output of f).
So the statement is:

FALSE

because it's partly backwards, and partly shifted; the domain is all reals, and the range is (-π/2, π/2).
[... so that both endpoints are excluded.]