Chapter 5: Q. 515 (page 564)

For the functions $f (x) = 3 x^{2} - 23 x - 36$ and $g (x) = x - 9$ find
(a) $\frac{f}{g} (x)$
(b)data-custom-editor="chemistry" $\frac{f}{g} (3)$

Short Answer

Expert verified

The required values are:

(a) $\frac{f}{g} (x) = 3 x + 4$

(b) $\frac{f}{g} (3) = 13$

Step by step solution

Step 1. Given Information

The given functions are $f (x) = 3 x^{2} - 23 x - 36$ and $g (x) = x - 9$

Part (a) Step 1. Divide the Functions

Divide f by gas shown below:
$\begin{matrix} x & - 9 \end{matrix} \begin{matrix} 3 x & + 4 \end{matrix} \begin{matrix} 3 x^{2} & - 23 x & - 36 \end{matrix} \begin{matrix} - & (3 x^{2} & - 27 x) \\ 4 x & - 36 \\ - & (4 x & - 36) \\ 0 \end{matrix}$
So, the function $\frac{f}{g} (x) = 3 x + 4$

Part (b) Step 1. Given Information

The given functions are $f (x) = 3 x^{2} - 23 x - 36$ and $g (x) = x - 9$ .

Part (b) Step 2. Substitution

Substitute $x = 3$ in $\frac{f}{g} (x) = 3 x + 4$ and solve.

localid="1644593038014" $\begin{array}{rcl} \frac{f}{g} (3) & = & 3 (3) + 4 \\ = & 13 \end{array}$

So, $\frac{f}{g} (3) = 13$ .

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For the functions $f (x) = 3 x^{2} - 23 x - 36$ and $g (x) = x - 9$ find
(a) $\frac{f}{g} (x)$
(b)data-custom-editor="chemistry" $\frac{f}{g} (3)$

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Divide the Functions

Part (b) Step 1. Given Information

Part (b) Step 2. Substitution

One App. One Place for Learning.

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For the functions fx=3x2-23x-36and g(x)=x-9find (a) fg(x)(b)data-custom-editor="chemistry" fg(3)

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Divide the Functions

Part (b) Step 1. Given Information

Part (b) Step 2. Substitution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Mechanics Maths

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Calculus

Probability and Statistics

Study anywhere. Anytime. Across all devices.

For the functions $f (x) = 3 x^{2} - 23 x - 36$ and $g (x) = x - 9$ find
(a) $\frac{f}{g} (x)$
(b)data-custom-editor="chemistry" $\frac{f}{g} (3)$