Question

If a(x) = 2x - 4 and b(x) = x 2, which of the following expressions produces a quadratic function?
i. (ab)(x)
ii. (ab)(x)
iii. (a−b)(x)
iv. (a+b)(x)

Answer 1

The expression $(a\cdot b)(x)$ produces a quadratic function. (Right choice: (i))

Note - The statement presents a typing error, the correct form is presented below:

If $a(x) = 2\cdot x - 4$ and $b(x) = x+2$, which of the following expressions produces a quadratic function?

(i) $(a\cdot b) (x)$

(ii) $\left(\frac{a}{b} \right) (x)$

(iii) $(a-b)(x)$

(iv) $(a+b) (x)$

In this question we must apply operations between functions. Since $a(x)$ is a first order polynomial and $b(x)$ is a second order polynomial. Then, we have the expected results:

• The addition of $a(x)$ and $b(x)$ equals a first order polynomial.
• The subtraction of $a(x)$ and $b(x)$ equals a first order polynomial.
• The multiplication of $a(x)$ and $b(x)$ equals a second order polynomial.
• The division of $a(x)$ by $b(x)$ equals a zero order polynomial.

Therefore, we conclude that the right choice is (i).

We kindly invite to see this question on functions: https://brainly.com/question/22804823