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Suppose f and g are functions with domain all real numbers. Which of the following statements is not necessarily true? = O (h+q)(x) = (a + h)(x) O (hq)(x) = (qh)(x) O (h – q)(x) = - (q - h)(x) O h(g(x)) = q(h(x)) O (h o q)(x) = h(q(x))



Answer :

The statement that is not necessarily true for the functions is given as follows:

h(q(x)) = q(h(x)).

What is said by each statement?


The first statement is relative to the commutative property of addition, which we know that it is true, that the order in which the terms are added does not change the result.

The second statement is about the commutative property of multiplication, which we also know that it is true, as the order in which the terms are multiplied does not change the product.

The third statement is about the subtraction, which we can verify as follows:

(h - q)(x) = h(x) - q(x) = -q(x) + h(x).

Which is true.

The fourth statement is the false statement, as the composition of two functions is not necessarily commutative, while the fifth statement is true, as it is the definition of the composition of two functions.

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