Question

If domain of f(x) is [1, 2], then the domain of 2 f log x is

Answer 1

you mean, " if domain of f(x) is [1, 2] , then the domain of 2f(logx) is " right ?

you should understand that, domain of f(x) = domain of kf(x)
e.g., domain is independent of coefficient of f(x).

so, domain of f(logx) = domain of 2f(logx)

now, as ' logx ' in place of 'x'

so, 1 ≤ logx ≤ 2

or, 10¹ ≤ x ≤ 10²

hence, 10 ≤ x ≤ 100

so, domain of 2f(logx) $\in$ [10, 100]