pls. help..
The functions f and g satisfy
f(x) + g(x) = 3x + 5
f(x) �� g(x) = 5x + 7
for all values of x. Determine the value of 2f(2)g(2).
To find the value of 2f(2)g(2), we need to determine the values of f(2) and g(2) first.
Given that f(x) + g(x) = 3x + 5, we can substitute x = 2 into this equation to find f(2) + g(2):
f(2) + g(2) = 3(2) + 5
f(2) + g(2) = 6 + 5
f(2) + g(2) = 11
Next, we are given that f(x) 〈 g(x) = 5x + 7. Substituting x = 2 into this equation will give us f(2) 〈 g(2):
f(2) 〈 g(2) = 5(2) + 7
f(2) 〈 g(2) = 10 + 7
f(2) 〈 g(2) = 17
Now we have obtained the values of f(2) + g(2) = 11 and f(2) 〈 g(2) = 17.
To find the value of 2f(2)g(2), we simply substitute f(2) = 11 and g(2) = 17 into the expression:
2f(2)g(2) = 2(11)(17)
2f(2)g(2) = 22 * 17
2f(2)g(2) = 374
Therefore, the value of 2f(2)g(2) is 374.