Question

f[g(x)] = g[f(x)] for any two functions.
(hint: Use f(x) = x + 1 and g(x) = x2).
Select one:
True
False

Answer 1

well \[f(g(x)) = f(x^2)\]

so in f(x) you replace x with x^2

so \[f(g(x)) = x^2 + 1\]

now for

g(f(x)) = g(x + 1)

so you replace x by x + 1

\[g(f(x)) = (x + 1)^2 = x^2 + 2x + 1\]

so you decide if they are the same...

Answer 2

true