Question

let f(x)= tan^(-1)x then the domain f(x) is all real numbers and the range is [0,pi], is this true or false?

Answer 1

What is the domain of tan(x)

Answer 2

any ideas?

Answer 3

pi/2?

Answer 4

that's a value that you restrict from the domain

this is because tan(pi/2) is undefined

Answer 5

same for -pi/2

Answer 6

so its false?

Answer 7

so the domain of tan(x) is the set of all real numbers, but multiples of pi/2 are excluded

Answer 8

if you just look at the first period of tan(x), it goes from -pi/2 to pi/2

Answer 9

the range of that piece is (-inf, inf)

Answer 10

so if you flip things around, the domain of arctan(x) is (-inf, inf)

and the range of arctan(x) is (-pi/2, pi/2)

Answer 11

so yes it's false because there are negative values in the range of arctan(x)

Answer 12

oooohh now I get it thank you

Answer 13

yeah a graph helps if you're not sure

Answer 14

yw