Question

Need help!!!

Determine the domain of the function (f*g)(x) where f(x) = 1/x , g(x) = sqrt(2-5x)

Answer 1

is this
\[(f\cdot g)(x) \text{ or } (f\circ g)(x)\]

Answer 2

the second one

Answer 3

so this is a composition of the functions.

so we'll get

\[(f \circ g)(x)=f(g(x))=\frac{ 1 }{ g(x) }=\frac{ 1 }{ \sqrt{2-5x} }\]

right?

Answer 4

yeah

Answer 5

so what has to happen?

Answer 6

remember... you're not allowed to divide by 0 and you can't have a negative number inside a square root.

Answer 7

The restriction is \(x \ne 0\) and \(x \ngeq \dfrac{2}{5}\)

Furthermore, I would rationalize the denominator.