f(x)=13x^2 -15x-14
g(x)=15x^3+14x^2-15x+12
find f(3) × f(10) + f(-7) × g(9)
f(3) = 13*9-15*3+4
and so on. Just plug in your x values and crank it out.
Move along folks -- nothing to see here...
To find f(3) × f(10) + f(-7) × g(9), we first need to find the values of f(x) and g(x) at the given values of x. Let's start by calculating f(3) and f(10):
f(x) = 13x^2 - 15x - 14
1. f(3):
Replace x with 3 in the equation:
f(3) = 13(3)^2 - 15(3) - 14
f(3) = 13(9) - 45 - 14
f(3) = 117 - 45 - 14
f(3) = 58
2. f(10):
Replace x with 10 in the equation:
f(10) = 13(10)^2 - 15(10) - 14
f(10) = 13(100) - 150 - 14
f(10) = 1300 - 150 - 14
f(10) = 1136
Next, let's calculate g(9):
g(x) = 15x^3 + 14x^2 - 15x + 12
3. g(9):
Replace x with 9 in the equation:
g(9) = 15(9)^3 + 14(9)^2 - 15(9) + 12
g(9) = 15(729) + 14(81) - 135 + 12
g(9) = 10935 + 1134 - 135 + 12
g(9) = 12006
Now that we have the values of f(3), f(10), and g(9), we can compute f(3) × f(10) + f(-7) × g(9):
f(3) × f(10) + f(-7) × g(9)
= 58 × 1136 + f(-7) × 12006
To find f(-7), we substitute x = -7 into the equation for f(x):
f(x) = 13x^2 - 15x - 14
4. f(-7):
Replace x with -7 in the equation:
f(-7) = 13(-7)^2 - 15(-7) - 14
f(-7) = 13(49) + 105 - 14
f(-7) = 637 + 105 - 14
f(-7) = 728
Now we can calculate the final result:
f(3) × f(10) + f(-7) × g(9)
= 58 × 1136 + 728 × 12006
Multiplying these values together will give us the answer.