Determine whether the equation defines y as a function of x?

Question

y= square root (4x-3)

a. y is a function of x ( I thnk this is the answer)

b. y is NOT a function of x

Answer 1

y = √(4x - 3) is a function of x as there is a unique value of y for every value of x in the domain of the function.

I would like to clarify some point here.

Whenever we say square-root in language, we mean both positive and negative square-roots and in that context y above will not be a function of x. But √(4x - 3) is always considered as a positive square-root and will be a function of x.

Answer 2

y= square root (4x-3) defines a function if and only if x ≥ 3/4

Answer 3

It all depends on the domain and co domain of the function. A sq rt has 2 values in general so its not a function with given information.

But if the domain is given to be all x> 3/4 andco domainn is given to be + ve reals only or (- ve reals only) then it is.

Answer 4

a. y is a function of x

Answer 5

I think its not, because If x = 0 then it the equation will be

y= square root (-3)

which doesn`t exist.

(you can`t take the square root of negative numbers)

so this is a function what its restricted

specifically when the domain is (3/4, infinity)

however, I`m not sure, so wait someone to confirm it.