Question

Let f, g : R → R be defined, respectively by f(x) = x + 1 and g(x) = 2x − 3. Find f + g, f − g and $\frac{f}{g}$.

Answer 1

f, g : R → R is defined, respectively, by f(x) = x + 1 and 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

$\left(\frac{f}{g}\right)\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)},g\left(x\right)\ne 0,x\in \mathit{R}$

$\mathbf{\Rightarrow }\left(\frac{f}{g}\right)\left(x\right)=\frac{x+1}{2x-3},2x-3\ne 0or2x\ne 3$

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