Answer:
-The composition of functions p and q is not commutative.
-Both p(q(x)) and q(p(x)) have the same domain.
-Graph A represents q(p(x))
Step-by-step explanation:
The statements that are true about the given composite functions are:
B) The composition of functions p and q is not commutative
D) Both p(q(x)) and q(p(x)) have the same domain i.e., x ∈ {R}
E) Graph A represents q(p(x)) = x³ + 5
The given functions are p(x) = x³ and q(x) = x + 5
Then the composite functions p(g(x)) and q(p(x)) are:
p(g(x)) = (x + 5)³ and
q(p(x)) = x³ + 5
where p(g(x)) and q(p(x)) are not commutative, since (a + b ≠ b + a) i.e.,
(x + 5)³ ≠ x³ + 5
The graphs for the functions p(x) and q(x) are shown in the figure below. The obtained composite functions are also drawn.
Thus, from the graph,
Graph A represents - q(p(x)) = x³ + 5
Graph B represents - p(q(x)) = (x + 5)³
So, options B, D, and E are true statements about the given graph.
Learn more about the composite functions here:
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