Question

show that the relation xy=-2 is a function for a suitable domain
find its domain and range

Answer 1

xy = -2 is hyperbolic equation . we can also write it y = -2/x or, f(x) = -2/x
A rough graph of f(x) = -2/x is shown in figure.
Here you can see that, f(x) satisfy the conditions of function.
because if we draw a vertical line [ parallel to y - axis ] , graph cuts just one point at any situations. It means, f(x) is function.

Now, domian of f(x) = -2/x
It is defined for all real numbers except x = 0
Hence, domain ∈ (-∞ , ∞) - {0}

And range of it is also all real number except y = 0
e.g., range ∈ (-∞, ∞) - {0}

Answer 2

Answer:

Step-by-step explanation:

xy = -2 is hyperbolic equation . we can also write it y = -2/x or, f(x) = -2/x

A rough graph of f(x) = -2/x is shown in figure.

Here you can see that, f(x) satisfy the conditions of function.

because if we draw a vertical line [ parallel to y - axis ] , graph cuts just one point at any situations. It means, f(x) is function.

Now, domian of f(x) = -2/x

It is defined for all real numbers except x = 0

Hence, domain ∈ (-∞ , ∞) - {0}

And range of it is also all real number except y = 0

e.g., range ∈ (-∞, ∞) - {0}