Question

2 part question
for f(x)=sqroot x and g(x)=x-3
1. find the function of (f/g)(x)
2. state the domain using interval notation

Answer 1

by definition, we can write:
\[\left( {\frac{f}{g}} \right)\left( x \right) = \frac{{f\left( x \right)}}{{g\left( x \right)}}\]

Answer 2

f(x) = sqrt(x)

g(x) = [sqrt(1-x)]^3 = (1-x)*sqrt(1-x).

Answer 3

so

Answer 4

that's right! @mlees1969

Answer 5

yes there aree many ways to do it but i prefer the easy way

Answer 6

now, the radical does exist if the subsequent condition holds:
\[x \geqslant 0\]
and we can't divide by zero, so we get this n:
\[x \ne 3\]
so what can you conclude?

Answer 7

and would the interval notation be