Answered

At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Explore a wealth of knowledge from professionals across various disciplines on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

If [tex]\( f(x) = 8 - 10x \)[/tex] and [tex]\( g(x) = 5x + 4 \)[/tex], what is the value of [tex]\( (f \circ g)(-2) \)[/tex]?

Sagot :

GinnyAnswer
Sure! Let's solve the problem step-by-step.

Given the functions:
[tex]\[ f(x) = 8 - 10x \][/tex]
[tex]\[ g(x) = 5x + 4 \][/tex]

We need to find the value of [tex]\((fg)(-2)\)[/tex], which means we need to evaluate the composite function [tex]\( f(g(-2)) \)[/tex].

Step 1: Evaluate [tex]\( g(-2) \)[/tex]

Substitute [tex]\( x = -2 \)[/tex] into the function [tex]\( g(x) = 5x + 4 \)[/tex]:
[tex]\[ g(-2) = 5(-2) + 4 \][/tex]

Perform the arithmetic operations:
[tex]\[ g(-2) = -10 + 4 \][/tex]
[tex]\[ g(-2) = -6 \][/tex]

Step 2: Evaluate [tex]\( f(g(-2)) \)[/tex] which is [tex]\( f(-6) \)[/tex]

Now we substitute [tex]\( x = -6 \)[/tex] into the function [tex]\( f(x) = 8 - 10x \)[/tex]:
[tex]\[ f(-6) = 8 - 10(-6) \][/tex]

Perform the arithmetic operations:
[tex]\[ f(-6) = 8 + 60 \][/tex]
[tex]\[ f(-6) = 68 \][/tex]

Therefore, the value of [tex]\( (fg)(-2) \)[/tex] is:
[tex]\[ \boxed{68} \][/tex]
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.