The problem is playing around with domains.
If [imath]f_5 = log(x^6)[/imath], what is the implied domain of [imath]f_5[/imath]?
For [imath]f_1[/imath] what is the implied domain of [imath]f_1[/imath]?
For [imath]f_2[/imath] what is the implied domain of [imath]f_2[/imath]?
For [imath]f_3[/imath] what is the implied domain of [imath]f_3[/imath]?
For [imath]f_4[/imath] what is the implied domain of [imath]f_4[/imath]?
If two functions have different domains can they be equal?
I must admit that I find it a trick question. The convention is that if no domain is specified, we are to assume the maximum feasible domain. The problem would be trivial if it had specified the relevant domains explicitly.