Question

Let f:{x: IxI > 100} => R, f(x) = 1/x^2. State the range of f.

Let f:{x: IxI < 0.1} => R, f(x) = 1/x^2. State the range of f.

*R = real numbers

How do you find the two ranges? I know it sounds embarrassing but I am struggling to work out the range. Can you please show your working?

Answer to (a) is [0, 1/(10^4)]
Answer to (b) is [100, infinity]

Answer 1

the domain is (-∞,-100)U(100,∞)
Since f(x) = 1/x^2, the range is the same on both those intervals. So, R = (0,1/100^2)

if the domain is (-0.1,0.1) then f(0) is undefined. The range is thus (1/0.1^2,∞) since f(x) is symmetric about x=0.