Question

if f(x)=x^2+3 and g(x)=3x-1
then find the following

1g. (f * g)(x)

1h. (f * g)(1)

1i. (g * f)(x)

Answer 1

If $f(x) = x^{2} + 3$ and $g(x) = 3x - 1$ then find the following

1g. $(f * g)(x)$

1h. $(f * g)(1)$

1i. $(g * f)(x)$

**Solution:**

1g. Composition $(f * g)(x)$ - means to multiply the two functions $f(x) * g(x)$.

$$(f * g)(x) = f(x) * g(x) = (x^{2} + 3)(3x - 1) = 3x^{3} - x^{2} + 9x - 3$$

1h. Determine the value of the product features for a given value $x$, evaluate when $x = 1$

$$\begin{array}{l} (f * g)(1) = 3(1)^{3} - 1(1)^{2} + 9 \cdot 1 - 3 = 8 \\ (f * g)(1) = 8 \\ \end{array}$$

1i. Since multiplication is commutative then both variants 1g and 1i will have the same answer.

$$(g * f)(x) = (f * g)(x) = (3x - 1)(x^{2} + 3) = 3x^{3} - x^{2} + 9x - 3$$