Question

Function h is the product of functions f and g. f(x) = 2x+5 g(x) = 6x − 9

which equation defines function h?
a. h(x) = 12x² − 45
b. h(x) = 12x − 45
c. h(x) = 12x² − 4x − 45
d. h(x) = 12x² 12x − 45

Answer 1

To find the product of functions f(x) and g(x), you multiply the functions together. The correct product h(x) is found to be 12x² + 12x - 45, making option (d) the correct answer.

Step-by-step explanation:

To find the function h, which is the product of functions f and g, we simply multiply the two given functions together. Given that f(x) = 2x + 5 and g(x) = 6x - 9, we can find h(x) using the following steps:

• Multiply the coefficients of the x terms: 2 * 6 = 12, so the x² coefficient for h(x) is 12.
• Multiply the outer terms: 2x * (-9) = -18x.
• Multiply the inner terms: 5 * 6x = 30x.
• Add the x terms: -18x + 30x = 12x.
• Multiply the constant terms: 5 * (-9) = -45.

Now, we can combine these results to write the function h(x):

h(x) = 12x² + 12x - 45

Comparing this result with the given options, the correct equation that defines function h is h(x) = 12x² + 12x - 45. Therefore, the correct choice is (d).