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

1 Answer
Jul 15, 2015

(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.