Find (f+g)(3), (f-g)(3), (fg)(3), and (f/g)(3) for f(x)=x+3, g(x)=x^2

Question

asked May 3, 2020 122k views

1 Answer

Joel Falcou · Answer 1 · 2020-05-10T20:34:04+0000

Answer:

15, -3, 54, 2/3

Explanation:

We have:

$f(x)=x+3\\g(x)=x^2$

(f+g)(x) can be calculated as

(f+g)(x)=f(x)+g(x)

So in this case,

(f+g)(x)=x+3+x^2

And substituting x = 3,

(f+g)(3)=3+3+3^2=15

(f-g)(x) can be calculated as

(f-g)(x)=f(x)-g(x)

So in this case,

(f-g)(x)=x+3-x^2

And substituting x = 3,

(f+g)(3)=3+3-3^2=-3

(fg)(x) can be calculated as

(fg)(x)=f(x)g(x)

So in this case,

(fg)(x)=(x+3)(x^2)=x^3+3x^2

And substituting x = 3,

$(fg)(3)=3^3+3\cdot 3^2=54$

(f/g)(x) can be calculated as

(f/g)(x)=(f(x))/(g(x))

So in this case,

(f/g)(x)=(x+3)/(x^2)

And substituting x = 3,

(f/g)(3)=(3+3)/(3^2)=(2)/(3)