Determine whether (f o g)(x) = x and whether (g o f)(x) = x. f(x) = (x +1)^2, g(x) = x^2?

Question

college algebra

Answer 1

The question doesn't make sense as set. The rules of the game need to be understood. Define "o"; or is this a font limitation? Are f and g to be interpreted as operators, with (f o g)(x) meaning "First find g(x), then find f[g(x)]", etc? Presumably, to avoid possible confusion, you also meant to put not "x.f(x)...etc", but rather "x, where f(x) = ... etc"

If so, then (f o g)(x) = (x^2 + 1)^2 and (g o f)(x) = (x + 1)^4.

Obviously, neither of these successive operations produces merely x; so both answers are a resounding NO!

Live long and prosper.

Answer 2

your question does make any sense because exponents will grow up!!!