Question

find $(f + g)(x)$, $(f - g)(x)$, $(f\cdot g)(x)$ and $(f/g)(x)$ for $f(x)$ and $g(x)$.
$f(x) = x^2$
$g(x) = x + 3$

Explanation:

Step1: Calculate $(f+g)(x)$

Substitute $f(x)$ and $g(x)$:
$(f+g)(x) = f(x) + g(x) = x^2 + (x + 3)$
Simplify: $(f+g)(x) = x^2 + x + 3$

Step2: Calculate $(f-g)(x)$

Substitute $f(x)$ and $g(x)$:
$(f-g)(x) = f(x) - g(x) = x^2 - (x + 3)$
Simplify: $(f-g)(x) = x^2 - x - 3$

Step3: Calculate $(f\bullet g)(x)$

Multiply $f(x)$ and $g(x)$:
$(f\bullet g)(x) = f(x) \cdot g(x) = x^2(x + 3)$
Expand: $(f\bullet g)(x) = x^3 + 3x^2$

Step4: Calculate $(f/g)(x)$

Divide $f(x)$ by $g(x)$, note domain restriction:
$(f/g)(x) = \frac{f(x)}{g(x)} = \frac{x^2}{x + 3}$, where $x
eq -3$

Answer:

$(f+g)(x) = x^2 + x + 3$
$(f-g)(x) = x^2 - x - 3$
$(f\bullet g)(x) = x^3 + 3x^2$
$(f/g)(x) = \frac{x^2}{x + 3}, \ x
eq -3$