Question

How do you find the domain of `[fog](x)` given `f(x)=1/x` and `g(x)=7-x`?

Answer 1

Domain of `[fog](x)`: `RR-{7}`

Explanation:

If `f(color(red)x)=1/color(red)x`
then `[fog](x)=f(color(red)(g(x)))=1/color(red)(g(x))`

which is defined for all values of `color(red)(g(x))!=0`

Since `color(red)(g(color(blue)x)=7-color(blue)x`
`color(white)("XXX")color(red)(g(color(blue)x))!=0color(white)("X")rarrcolor(white)("X")color(blue)x!=7`

That is `[fog](x)` is defined for all real values of `x` except `x=7`