Question

find the domain of f(x)^-1 if f(x)=3/x-2 is it 0, -2, or 3? or all real numbers?

Answer 1

domain of the inverse is the range of the original function
it may not be obvious what the range of \(f\) is, but it is all real numbers except 0, because a fraction is only 0 if the numerator is, and your numerator is 3

Answer 2

so its all real numbers?

Answer 3

therefore the domain of \(f^{-1}(x)\) is all numbers except 0
you would also see this if you solve for \(f^{-1}\) explicitly

Answer 4

it is all real numbers except 0

Answer 5

ok thanks!

Answer 6

yw