I am beyond confused

[Loki123]

Somebody please help me with this because I think I have gone insane. You are given 4 functions, right after = is what the question gives us, after the second = is how I simplified it.
I think f1=f2=f3=f4 which apparently is not correct. How?

 

[BigBeachBanana]

Somebody please help me with this because I think I have gone insane. You are given 4 functions, right after = is what the question gives us, after the second = is how I simplified it.
I think f1=f2=f3=f4 which apparently is not correct. How? View attachment 30488

Because for functions 2 and 4, x can take on negative values.

 

[JeffM]

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.

 

[Loki123]

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.

Thank you, I see now.