Math problem

Question

What is the domain of the function f(x)= (1/3)log (2 square root of 2x-10)

                                                                       3

I found (-5/4,∞) is this correct?

Answer 1

f(x) = (1/3)log₃(2√(2x-10))

 

If f(x) is a real number, We can't take square roots of negative numbers and we can only find the log of a positive number.

 

So, domain f = {x l 2x-10 > 0}

 

                   = {x l x > 5}  = (5,∞) 

Answer 2

For 2√(2x - 10),

2x - 10 ≥ 0

That is x ≥ 5

The domain [5, ∞)