Answer:
In general gf(x) is not equal to fg(x)
Some pairs of functions cannot be composed. Some pairs of functions can be composed only for certain values of x.
Only with they can be composed some values of x are the ranges of g(x) and f(x) are the same, and their domains are also the same. Or else lies inside it.
Step-by-step explanation:
g(x) = 3x + 6 - 8, f(x) = √x.
The domain of a composed function is either the same as the domain of the first function, or else lies inside it
The range of a composed function is either the same as the range of the second function, or else lies inside it.
Or vice versa
Now only positive numbers, or zero, have real square roots. So g is defined only for numbers
greater than or equal to zero. Therefore g(f(x)) can have a value only if f(x) is greater than or
equal to zero. You can work out that
f(x) ≥ 0 only when x ≥3/2
.
