Question

domain of the function 1/sqrt(15x + 12) pls

Answer 1

Domain: Generally think of All Real Numbers and then see if you have to throw out anything.

Common "throw-outs" are these.

What makes a denominator zero?
Logarithms need positive arguments.
Even roots need non-negative arguments.

Various other things, but these will do for this problem. What say you? What shall we discard?

Answer 2

is it [78,inf)?

Answer 3

No. Far too much has been discarded. Tell me how you managed that result?

Answer 4

15x+12=0

15x=-12
x=-12/15

Answer 5

is it (-12/15,inf) then?

Answer 6

That is correct, but it is not a logical conclusion from your work.

You need 15x + 12 > 0

This leads to x > -12/15 and is logically translated to \(\left(-\dfrac{12}{15},\infty\right)\)

Answer 7

thanks very much

Answer 8

what about this\[\sqrt[3]{t-78}\]
what is the domain in interval notation please