Question

In Exercises $1-8,$ compute each expression, given that the functions $f, g, h, k,$ and $m$ are defined as follows: $$\begin{array}{ll} f(x)=2 x-1 & k(x)=2, \quad \text { for all } x \\ g(x)=x^{2}-3 x-6 & m(x)=x^{2}-9 \\ h(x)=x^{3} \end{array}$$ (a) $(f g)(x)$ (b) $(f g)(1 / 2)$

Name: Problem 4, Chapter 3: Precalculus
Uploaded: 2020-07-15T19:48:25-08:00
Duration: 2 min 17 s
Channel: Sarah X
Description: In Exercises 1-8, compute each expression, given that the functions f, g, h, k, and m are defined as follows: f(x)=2 x-1 k(x)=2, for all x g(x)=x^2-3 x-6 m(x)=x^2-9 h(x)=x^3 (a) (f g)(x) (b) (f g)(1 / 2)

   In Exercises $1-8,$ compute each expression, given that the functions $f, g, h, k,$ and $m$ are defined as follows:
$$\begin{array}{ll} f(x)=2 x-1 & k(x)=2, \quad \text { for all } x \\ g(x)=x^{2}-3 x-6 & m(x)=x^{2}-9 \\ h(x)=x^{3} \end{array}$$
(a) $(f g)(x)$
(b) $(f g)(1 / 2)$

Precalculus

David Cohen,… 7th Edition

Chapter 3, Problem 4

Instant Answer

Solved by Expert Sarah X

07/15/2020

Step 1

This means we need to multiply the function $f(x)$ by the function $g(x)$. From the given functions, we know that $f(x) = 2x - 1$ and $g(x) = x^{2} - 3x - 6$. Show more…

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In Exercises $1-8,$ compute each expression, given that the functions $f, g, h, k,$ and $m$ are defined as follows: $$\begin{array}{ll} f(x)=2 x-1 & k(x)=2, \quad \text { for all } x \\ g(x)=x^{2}-3 x-6 & m(x)=x^{2}-9 \\ h(x)=x^{3} \end{array}$$ (a) $(f g)(x)$ (b) $(f g)(1 / 2)$

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Key Concepts

Function Evaluation

Function evaluation is the process of substituting a specific input value into a function to obtain an output. For instance, after forming the product function (fg)(x), you evaluate it at a specific input, such as x = 1/2, by computing f(1/2) and g(1/2) and then taking their product. This concept is fundamental in understanding how functions behave for particular inputs.

Function Multiplication

This concept involves creating a new function by multiplying the outputs of two functions for each input value. If f(x) and g(x) are given, then their product function (fg)(x) is defined as f(x) multiplied by g(x). This operation is important as it allows for combining functions in a way that can model more complex relationships between variables.

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