polismayven
Answered

At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Our Q&A platform provides quick and trustworthy answers to your questions from experienced professionals in different areas of expertise. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

If [tex][tex]$f(x)=2x$[/tex][/tex] and [tex][tex]$g(x)=x^3$[/tex][/tex], what is [tex][tex]$(f \circ g)(-3)$[/tex][/tex]?

A. -6
B. -27
C. 54
D. -54

Sagot :

GinnyAnswer
To solve the problem and find [tex]\((f \circ g)(-3)\)[/tex], let's break it down step by step.

Firstly, let's understand what [tex]\((f \circ g)(x)\)[/tex] means. This notation is read as "f of g of x," which means we need to first apply the function [tex]\(g(x)\)[/tex] and then apply the function [tex]\(f\)[/tex] to the result obtained from [tex]\(g(x)\)[/tex].

We have the functions:
[tex]\[ g(x) = x^3 \][/tex]
[tex]\[ f(x) = 2x \][/tex]

Step 1: Evaluate [tex]\(g(-3)\)[/tex]
[tex]\[ g(-3) = (-3)^3 = -27 \][/tex]

Step 2: Use the result from Step 1 as the input for the function [tex]\(f\)[/tex]:
[tex]\[ f(g(-3)) = f(-27) \][/tex]

Step 3: Evaluate [tex]\(f(-27)\)[/tex]
[tex]\[ f(-27) = 2 \times -27 = -54 \][/tex]

Therefore, [tex]\((f \circ g)(-3) = -54\)[/tex].

The correct answer is:
D. -54
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.