Find the function and domain?

Question

A. f+g. B. f-g. C. fxg. D. f/g

1.f(x)=2x+1
g(x)= 3x-2

Answer 1

Given f(x) = 2x+1

         g(x)= 3x-2

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

           = (2x+1) + (3x-2)

           = 5x-1

f+g = 5x-1

Domain of a function f(x) + g(x) is set of those values of x which will make the function mathematically legal or correct. 

So the domain is set of all real numbers

B) f - g = f(x) -  g(x)

           = (2x+1) - (3x-2)

           = -x+3

f - g = -x+3

Domain of a function f(x) - g(x) is set of those values of x which will make the function mathematically legal or correct. 

So the domain is set of all real numbers

C) f x g = f(x) x g(x)

             = (2x+1) x (3x-2)

             = 6x² +3x -4x -2

             = 6x² -x -2

f x g  = 6x² -x -2

Domain of a function f(x) x g(x) is set of those values of x which will make the function mathematically legal or correct. 

So the domain is set of all real numbers

D) f / g = f(x) / g(x)

             = (2x+1) / (3x-2)

f /g = (2x+1) / (3x-2)

Domain of a function f(x) / g(x) is set of those values of x which will make the function mathematically legal or correct.certain operations like division by zero , square root of a negative number do not exist in real maths.

So now Domain excludes x - values that result in division by zero.

3x-2 =0

3x = 2

x = 2/3

Domain is set of all real numbers except at x = 2/3