Answer:
f * g)(x) = 8x^2 - 2x - 15
Explanation:
Since we want to find (f * g)(x), we want to multiply the entire functions and leave the answer in terms of x (in terms of x simply means we do the multiplication and the simplified answer will be in terms of x):
Thus, we have (2x - 3)(4x + 5). This is a binomial expression and we can multiply binomials using the FOIL method, where
- "F" refers to the first terms (2x and 4x in this case),
- "O" refers to the outer terms (2x and 5),
- "I" refers to the inner terms (-3 and 4x),
- and "L" refers to the last terms (-3 and 5)
We add all the terms and combine like terms to find (f * g)(x):
(2x * 4x) + (2x * 5) + (-3 * 4x) + (-3 * 5)
8x^2 + 10x - 12x - 15
8x^2 - 2x - 15
Thus, (f * g)(x) is 8x^2 - 2x - 15