Find the range of the fuction f(x) = x^(2) - 2x -4`

Explanation

Let `x^(2)-2x - 4 = y`
or ` x^(2) - 2x - 4 - y = 0`
Now if x is real, then
`Dge 0`
`rArr (-2)^(2) - 4(1) (-4-y) ge 0`
or `4 + 16 + 4y ge 0`
or y`gt -5 `
Hence, range of `f(x) ` is [ -5, `infty`).
Alternate method: `f(x) = x^(2) - 2x -4`
`=(x -1)^(2) -5`
`ge-5`
Hence , range is `[-5, infty)`