Question

Let f, g: R → R be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Find f + g, f – g and f/g​

Answer 1

$\tt Let\:f,g:R \longrightarrow R \: is \: defined\: as \\ \tt f(x) = x + 1 \: , \: g(x) = 2x -3 \\ \\ \tt (f+g)(x) = f(x) + g(x) \\ \\ \tt \implies (f+g)(x) = x+1 + 2x-3 \\ \\ \tt \implies (f+g)(x) = 3x - 2 \\ \\ \tt \therefore \boxed{\bold{\underline{\red{\tt (f+g)(x) = 3x-2 }}}} \\ \\ \tt (f-g)(x) = f(x)-g(x) \\ \\ \tt \implies (f-g)(x) = x+1-(2x-3) \\ \\ \tt \implies (f-g)(x) = x +1 - 2x +3 \\ \\ \tt \implies (f-g)(x) = - x +4 \\ \\ \tt \therefore \boxed{\bold{\underline{\red{\tt (f-g)(x) = -x +4 }}}} \\ \\ \tt (\frac{f}{g})(x) = \frac{f(x)}{g(x)} \:\:\: g(x)≠ 0 \\ \\ \tt (\frac{f}{g})(x) = \frac{x+1}{2x-3} \:\:\: 2x - 3 ≠ 0 \\ \\ \tt \implies (\frac{f}{g})(x) = \frac{x+1}{2x-3} \:\:\: x≠\frac{3}{2} \\ \\ \tt \therefore \boxed{\bold{\underline{\red{\tt (\frac{f}{g})(x) = \frac{x+1}{2x - 3} \:\:\: x ≠ \frac{3}{2} }}}}$