Question

(f○g)(x)=√(1-3x²)/(2x-8) and (g○f)(x)=(1-3x²)/(3-2x²) . How to find f(g(4))?

Answer 1

`(f@g)(x)` is an alternate way of writing `f(g(x))` and is undefined when `x=4`

Explanation:

`f(g(x))` is the same as `(f@g)(x)`

So
`f(g(4))` is the same as `(f@g)(4)`

But
`(f@g)(x) = sqrt(1-3x^2)/(2x-8)`
`color(white)("XXXX")` `color(white)("XXXX")`...or `sqrt((1-3x^2)/(2x-8))`
`color(white)("XXXX")` `color(white)("XXXX")`it's hard to guess the range of the root symbol
`color(white)("XXXX")` `color(white)("XXXX")`and doesn't make any difference in this case, since...
When `x=4`
`color(white)("XXXX")`we have an attempt to divide by zero
`color(white)("XXXX")`which is undefined.