karinalo23
Answered

Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Given [tex]\( f(x) = 3x - 1 \)[/tex] and [tex]\( g(x) = 2x - 3 \)[/tex], for which value of [tex]\( x \)[/tex] does [tex]\( g(x) = f(2) \)[/tex]?

A. [tex]\( x = \frac{3}{2} \)[/tex]
B. [tex]\( x = 2 \)[/tex]
C. [tex]\( x = \frac{5}{2} \)[/tex]
D. [tex]\( x = 4 \)[/tex]

Sagot :

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

We are given two functions:
[tex]\[ f(x) = 3x - 1 \][/tex]
[tex]\[ g(x) = 2x - 3 \][/tex]

We need to find a value of [tex]\( x \)[/tex] such that:
[tex]\[ g(x) = f(2) \][/tex]

Let's start by evaluating [tex]\( f(2) \)[/tex]:
[tex]\[ f(2) = 3(2) - 1 \][/tex]
[tex]\[ f(2) = 6 - 1 \][/tex]
[tex]\[ f(2) = 5 \][/tex]

Now, we need to find the value of [tex]\( x \)[/tex] for which:
[tex]\[ g(x) = 5 \][/tex]

Substitute [tex]\( 5 \)[/tex] into the [tex]\( g(x) \)[/tex] function:
[tex]\[ 2x - 3 = 5 \][/tex]

To solve for [tex]\( x \)[/tex], add 3 to both sides of the equation:
[tex]\[ 2x - 3 + 3 = 5 + 3 \][/tex]
[tex]\[ 2x = 8 \][/tex]

Now, divide both sides by 2:
[tex]\[ \frac{2x}{2} = \frac{8}{2} \][/tex]
[tex]\[ x = 4 \][/tex]

Therefore, the value of [tex]\( x \)[/tex] that satisfies the equation [tex]\( g(x) = f(2) \)[/tex] is:
[tex]\[ \boxed{4} \][/tex]
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.