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 $\frac{f}{g}.$

Answer 1

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

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

= x + 1 + 2x - 3 = 3x - 2

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

= x + 1 - 2x + 3 = - x + 4

$\frac{\left(f\right)}{\left(g\right)}\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}=\frac{x+1}{2x-3},x\ne \frac{3}{2}$