Not sure how to set up these functions to solve the problem. Given: f(x)=3x+(1/x-1) & g(x)=2x+1. Find the following:?

2015-08-29 8:05 pm

1. (f+g)(x)
2. (f+g)(2)
3. (f-g)(x)
4. (f-g)(2)
5. (fg)(x)
6. (fg)(2)
7. (f/g)(x)
8. (f/g)(1)
9. (g/f)(x)
10. (g/f)(1/2)
You don't have to answer them all. just enough for me to understand how to set them up. thanks!

更新1:

f(x)=3x+(1/(x-1))

回答 (1)

lenpol7

2015-08-29 10:02 pm

✔ 最佳答案

(f + g)(x) = 3x + (1/(x - 1)) + (2x + 1)
(f + g)(x) = 5x + 1 + 1/(x + 1)
(f + g)(x) = (5x(x + 1) + 1(x+1) + 1) / (x + 1)
(f + g)(x) = 5x^2 + 5x + x + 1 + 1) / ( x + 1)
(f + g)(x) = (5x^2 + 6x + 2) / ( x + 1)

#2
(f + g)(2) = (5(2)^2 + 6(2) + 2) / ( 2+1)
(f + g)(2) = ( 20 + 12 + 2) / (3)
(f + g)(2) = 34/3

f - g you subtract the two functions
fg you multiply the two functions together
f/g divide 'f' by 'g'
g/f divide 'g' by 'f'

Then in each case substitute the '2' to obtain the numerical answer.

👍 1 👎 1