For functions f(x)=2 x-7 g(x)=2 x+7, find (a) (f ·g)(x) (b) (f ·g)(-3)

Name: Problem 280, Chapter 5: Intermediate Algebra
Uploaded: 2022-09-26T07:27:55-08:00
Duration: 2 min 11 s
Channel: Robin R
Description: For functions f(x)=2 x-7 g(x)=2 x+7, find (a) (f ·g)(x) (b) (f ·g)(-3)

step 1 So in this problem, you're given F of X and G of X, and you're supposed to find F times G of X.

Question

For functions $\quad f(x)=2 x-7$ $g(x)=2 x+7,$ find (a) $(f \cdot g)(x)$ (b) $(f \cdot g)(-3)$

   For functions $\quad f(x)=2 x-7$
$g(x)=2 x+7,$ find
(a) $(f \cdot g)(x)$
(b) $(f \cdot g)(-3)$

Intermediate Algebra

Lynn Marecek 2nd Edition

Chapter 5, Problem 280

Instant Answer

Solved by Expert Robin R

09/26/2022

Step 1

This is done by multiplying the two functions together. We have: \begin{align*} (f \cdot g)(x) &= f(x) \cdot g(x) \\ &= (2x - 7) \cdot (2x + 7) \\ &= 4x^2 + 14x - 14x - 49 \\ &= 4x^2 - 49 \end{align*} Show more…

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For functions $\quad f(x)=2 x-7$ $g(x)=2 x+7,$ find (a) $(f \cdot g)(x)$ (b) $(f \cdot g)(-3)$

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Key Concepts

Function Multiplication

This concept involves combining two functions by multiplying their outputs for a given input. In many contexts, it is important to understand that the product of functions f(x) and g(x) is a new function defined by multiplying f(x) by g(x). This operation is essential for building more complex functions from simpler ones and is a fundamental operation in algebra and calculus.

Function Evaluation

Function evaluation is the process of determining the output of a function for a particular input value. It involves substituting a specific value into the function's formula, thereby computing the corresponding result. This skill is crucial in mathematics, as it is used to analyze function behavior, verify solutions, and apply functions to real-world problems.

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