Question

Let f, g:R$\to$R be defined, respectively by f(x) = x+1, g(x) = 2x-3. Find f+g, f-g and $\frac fg$.

Answer 1

f, g: R$\to$R is defined as f(x) = x+1, g(x) = 2x-3
(f+g)(x) = f(x) + g(x) = (x+1) + (2x-3) = 3x-2
∴ (f+g)(x) = 3x-2

(f-g)(x) = f(x) - g(x) = (x+1) - (2x-3) = x+1-2x+3 = - x+4
∴ (f-g)(x) = -x+4

($\frac fg$)(x) = $\frac {f(x)}{g(x)}$, g(x)≠0,x∈R
($\frac fg$)(x) = $\frac {x+1}{2x-3}$, 2x-3≠0 or 2x≠3
($\frac fg$)(x) = $\frac {x+1}{2x-3}$, x≠$\frac 32$