Let `f:(R-{0})toR:f(x)=(1)/(x)` for all values of `x""inR-{0}`.
Find its domain and range. Also draw its graph.

Explanation

Let `f:(R-{0})toR:f(x)=(1)/(x)` . Then,
dom `(f)=R-{0}" and range "(f)R-{0}`.
We have:

On a graph paper, let X' OX and YOY' be the x-axis and the y-axis respectively.
We take the scale: 10 small divisions = 1 units.
Now we plot the points A(-4.-0.25), B(-2,-0.5), C(-1,-1), D(-0.5,02), E(-0.25,-4) and F(0.25,4), G(0.5,2), H(1,1), J(2,0.5) and K(4,0.25).

We join A, B, C, D and E freehand successiely to obtain a curve. Also, we join F, G, H, J and K freehand successively to obtain another curve, as shown above.