Q.If $f(x) = x^2 + 1$ and $g(x) = 2x - 3$, find $(f+g)(x)$, $(f-g)(x)$, $(fg)(x)$ and $\left(\dfrac{f}{g}\right)(x)$, stating the domain of the quotient.

Step 1: $(f+g)(x)=(x^2+1)+(2x-3)=x^2+2x-2$.

Step 2: $(f-g)(x)=(x^2+1)-(2x-3)=x^2-2x+4$.

Step 3: $(fg)(x)=(x^2+1)(2x-3)=2x^3-3x^2+2x-3$.

Step 4: $\left(\dfrac{f}{g}\right)(x)=\dfrac{x^2+1}{2x-3}$; since $g(x)=2x-3=0$ at $x=\dfrac{3}{2}$, this quotient is undefined there, so its domain is $\mathbb{R}-\left\{\dfrac{3}{2}\right\}$ (both $f$ and $g$ have domain $\mathbb{R}$, so no further restriction is ne …

Add, subtract and multiply the two formulas directly; for the quotient, form the ratio and separately find wh …

• Sign errors when subtracting $(2x-3)$, e.g. writing $-2x-3$ instead of $-2x+3$. …