Answer:
d. (g*f)(-9)=-1
Step-by-step explanation:
In this problem, we have two functions:
and
The notation:
(f*g)(x) represents the composite function of f and g; this can be calculated by using the output of g(x) as input for f(x), in other words:
Simiarly, the notation (g*f)(x) can be calculated by using the output of f(x) as input for g(x), mathematically:
Using the definitions of f(x) and g(x), we can derive an expression for the two composite functions here:
And
Now we can analyze the given statements:
a. (f*g)(2)=2 --> FALSE, because
b. (g*f)(2)=0 --> FALSE, because
c.(f*g)(9)=1 --> FALSE, because
d. (g*f)(-9)=-1 --> TRUE, because