The functions $$ f, g $$, and $$ h $$ are defined as follows. $$ f(x)=\frac{x^{3}+12}{x^{3}} \quad g(x)=|-10+4 x| \quad h(x)=\sqrt{1+5 x} $$ Find $$ f(-3), g\left(-\frac{3}{2}\right) $$, and $$ h(2) $$. Simplify your answers as much as possible. $$ g\left(-\frac{3}{2}\right)=\square $$

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We are given the functions

$$
f(x)=\frac{x^{3}+12}{x^{3}}, \quad g(x)=|-10+4x|, \quad h(x)=\sqrt{1+5x}.
$$

**Step 1: Compute $$ f(-3) $$**

Substitute $$ x = -3 $$:

$$
f(-3)=\frac{(-3)^{3}+12}{(-3)^{3}}.
$$

Calculate $$(-3)^{3}$$:

$$
(-3)^{3}=-27.
$$

Then,

$$
f(-3)=\frac{-27+12}{-27}=\frac{-15}{-27}=\frac{15}{27}.
$$

Simplify the fraction by dividing numerator and denominator by 3:

$$
f(-3)=\frac{15 \div 3}{27 \div 3}=\frac{5}{9}.
$$

---

**Step 2: Compute $$ g\left(-\frac{3}{2}\right) $$**

Substitute $$ x = -\frac{3}{2} $$:

$$
g\left(-\frac{3}{2}\right)=\left|-10+4\left(-\frac{3}{2}\right)\right|.
$$

Simplify inside the absolute value:

$$
4\left(-\frac{3}{2}\right)=-6,
$$

so

$$
g\left(-\frac{3}{2}\right)=\left|-10-6\right|=\left|-16\right|=16.
$$

Thus,

$$
g\left(-\frac{3}{2}\right)=\boxed{16}.
$$

---

**Step 3: Compute $$ h(2) $$**

Substitute $$ x = 2 $$:

$$
h(2)=\sqrt{1+5(2)}=\sqrt{1+10}=\sqrt{11}.
$$

---

Final simplified answers:

$$
f(-3)=\frac{5}{9}, \quad g\left(-\frac{3}{2}\right)=16, \quad h(2)=\sqrt{11}.
$$
$$ g\left(-\frac{3}{2}\right)=16 $$

The functions \( f, g \), and \( h \) are defined as follows. \[ f(x)=\frac{x^{3}+12}{x^{3}} \quad g(x)=|-10+4 x| \quad h(x)=\sqrt{1+5 x} \] Find \( f(-3), g\left(-\frac{3}{2}\right) \), and \( h(2) \). Simplify your answers as much as possible. \( g\left(-\frac{3}{2}\right)=\square \)

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