Rational and irrational

Question

My math teacher hust gave a problem in which f(x)= 2x^2+3x-1 ang g(x)= 3x+4 over 2x^2 and I need to find (f+g)(3),(f-g)(7), (f*g)(1/2) (f/g)(5) and (f o g)(3). The problem is that g(x) is a rational function so thats why I dontnknow how to solve irrational and rational function.. i need help

Answer 1

f+g = 2x^2 + 3x - 1 + (3x+4)/(2x^2) at x=3

2*3^2 + 3(3) - 1 + (3*3+4)/(2*3^2) =

2 * 9 + 9 - 1 + (13)/18 =

18 + 9 - 1 + 13/18 =

26 + 13/18

f-g = 2x^2 + 3x - 1 - (3x+4)/(2x^2) at x=7

2(7)^2 + 3(7) - 1 - (3*7+4)/(2*7^2)=

2*49 + 21 - 1 - (25/98) =

98 + 21 - 1 - (25/98) =

118 - 25/98 =

117 + 73/98

f * g = (2x^2+3x-1)(3x+4)/2x^2 at x = 1/2

[2 * (1/2)^2 + 3 * (1/2) - 1 ][ 3 (1/2) + 4] / ( 2(1/2)^2)

[ 1/2 + 3/2 - 1][ 3/2 + 4] / (1/2)

1 * 11/2 / (1/2) =

11/2 / 1/2 = 11

f/g = (2x^2+3x-1)*(2x^2)/ (3x+4) at x=5

(2*25 + 15 - 1)* 50 / 19

64*50/19

3200 / 19

g(3) = [3(3)+4]/(2*9) = 13/18

f(13/18) = 2 ( 13/18)^2 + 3(13/18) - 1 =

2 ( 169/324) + 39/18 - 1=

338/324 + 39/18 - 1 =

338/324 + 39*18/ 324 - 324/324 =

(338 + 702 - 324)/324 =

716/324

358/162

179/81