The range of function f (x) = | lgx 2-lgx | (x > 0) |1 lgx| In the title (| lgx 2-lgx |) and (| 1 lgx |) are aligned, similar to the appearance of the matrix, which is in an absolute value

It's not a matrix; it's called determinant
The second-order determinant operates as follows:
|a b|=ad-bc
|c d|
be
|lgx 2-lgx|
|1 lgx |
=（lgx）^2-1·(2-lgx)
=（lgx）^2+lgx-2
=(lgx+1/2)^2-9/4
If lgx ∈ R, then
Lgx + 1 / 2 ∈ R. then
f(x)=(lgx+1/2)^2-9/4≥-9/4.
So the range of F (x) is [- 9 / 4, + ∞)

The range of function f (x) = | lgx 2-lgx | (x > 0) |1 lgx| In the title (| lgx 2-lgx |) and (| 1 lgx |) are aligned, similar to the appearance of the matrix, which is in an absolute value

The range of function f (x) = | lgx 2-lgx | (x > 0) |1 lgx| In the title (| lgx 2-lgx |) and (| 1 lgx |) are aligned, similar to the appearance of the matrix, which is in an absolute value

RELATED INFORMATIONS