Suppose that the functions $$ h $$ and $$ g $$ are defined as follows. $$ \begin{array}{l}h(x)=-4+3 x^{2} \ g(x)=4-9 x\end{array} $$ (a) Find $$ \left(\frac{h}{g}\right)(-5) $$. (b) Find all values that are NOT in the domain of $$ \frac{h}{g} $$. If there is more than one value, separate them with commas. (a) $$ \left(\frac{h}{g}\right)(-5)=\square $$ (b) Value(s) that are NOT in the domain of $$ \frac{h}{g}: \square $$

Question

UpStudy AI · Accepted Answer

To solve the problem, we will follow the steps outlined:

### Part (a): Find $$ \left(\frac{h}{g}\right)(-5) $$

1. **Calculate $$ h(-5) $$**:
   $$
   h(x) = -4 + 3x^2
   $$
   Substituting $$ x = -5 $$:
   $$
   h(-5) = -4 + 3(-5)^2 = -4 + 3(25) = -4 + 75 = 71
   $$

2. **Calculate $$ g(-5) $$**:
   $$
   g(x) = 4 - 9x
   $$
   Substituting $$ x = -5 $$:
   $$
   g(-5) = 4 - 9(-5) = 4 + 45 = 49
   $$

3. **Calculate $$ \left(\frac{h}{g}\right)(-5) $$**:
   $$
   \left(\frac{h}{g}\right)(-5) = \frac{h(-5)}{g(-5)} = \frac{71}{49}
   $$

### Part (b): Find all values that are NOT in the domain of $$ \frac{h}{g} $$

The function $$ \frac{h}{g} $$ is undefined when $$ g(x) = 0 $$. We need to find the values of $$ x $$ for which $$ g(x) = 0 $$:

1. **Set $$ g(x) = 0 $$**:
   $$
   4 - 9x = 0
   $$

2. **Solve for $$ x $$**:
   $$
   9x = 4 \implies x = \frac{4}{9}
   $$

### Final Answers

(a) $$ \left(\frac{h}{g}\right)(-5) = \frac{71}{49} $$

(b) Value(s) that are NOT in the domain of $$ \frac{h}{g}: \frac{4}{9} $$
(a) $$ \left(\frac{h}{g}\right)(-5) = \frac{71}{49} $$ (b) $$ \frac{4}{9} $$

Suppose that the functions and are defined as follows.

(a) Find .
(b) Find all values that are NOT in the domain of .
If there is more than one value, separate them with commas.
(a)
(b) Value(s) that are NOT in the domain of

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Solución

Part (a): Find

Part (b): Find all values that are NOT in the domain of

Final Answers

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Suppose that the functions and are defined as follows. (a) Find . (b) Find all values that are NOT in the domain of . If there is more than one value, separate them with commas. (a) (b) Value(s) that are NOT in the domain of