Find the following fx x2 gx 3x 5 f g1 f g2 f middot g

Find the following. f(x) = x^2, g(x) = 3x - 5 (f + g)(1) = (f - g)(2) = (f middot g) (x) = (f/g)(x) = Find the domain of (f/g) (x)

Solution

f(x)= x²
g(x)= 3x-5

a) f+g (1) = f(1) + g(1) = 1² + 3(1)-5 = 1+3-5= -1; f+g (1) = -1;
b)  f-g (2) = f(2) - g(2) = 2²- (3*2-5) = 2²-3*2+5= 4-6+5= 3; Hence f-g (2) =3;
c) f.g (x) = f(x)* g(x) = x²* ( 3x-5) = 3x³-5x2
d) (f/g) (x) = f(x)/ g(x) = x²/(3x-5); This will be defined only when 3x-5 is not equal to zero. Thus 3x is not equal to 5 and x is not equal to 5/3. Hence, (f/g) (x) = x²/ 3x-5 such that x is not = 5/3
e) fg (x) = f(g(x)) so g(x) = 3x- 5 so f(3x-5) = (3x-5)²; Hence fg = (3x-5)²