Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
To solve the given problem [tex]\( f\left(\frac{3 x-1}{2}\right)=6 x+1 \)[/tex] and find the value of [tex]\( f(2) \)[/tex], we can follow these steps:
1. Set the expression inside the function equal to 2:
[tex]\[ \frac{3x - 1}{2} = 2 \][/tex]
2. Solve for [tex]\(x\)[/tex]:
- First, multiply both sides of the equation by 2 to clear the fraction:
[tex]\[ 3x - 1 = 4 \][/tex]
- Next, add 1 to both sides to isolate the [tex]\(3x\)[/tex] term:
[tex]\[ 3x = 5 \][/tex]
- Now, divide both sides by 3 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{5}{3} \][/tex]
3. Substitute [tex]\(x = \frac{5}{3}\)[/tex] back into the function [tex]\(f\left(\frac{3 x-1}{2}\right)=6 x+1\)[/tex] to find [tex]\( f(2) \)[/tex]:
- The given function can be rewritten with [tex]\(x = \frac{5}{3}\)[/tex]:
[tex]\[ f\left(2\right) = 6 \left(\frac{5}{3}\right) + 1 \][/tex]
- Simplify inside the parenthesis:
[tex]\[ f(2) = 2 \times 5 + 1 \][/tex]
[tex]\[ f(2) = 10 + 1 \][/tex]
[tex]\[ f(2) = 11 \][/tex]
Hence, the value of [tex]\( f(2) \)[/tex] is [tex]\( 11 \)[/tex].
1. Set the expression inside the function equal to 2:
[tex]\[ \frac{3x - 1}{2} = 2 \][/tex]
2. Solve for [tex]\(x\)[/tex]:
- First, multiply both sides of the equation by 2 to clear the fraction:
[tex]\[ 3x - 1 = 4 \][/tex]
- Next, add 1 to both sides to isolate the [tex]\(3x\)[/tex] term:
[tex]\[ 3x = 5 \][/tex]
- Now, divide both sides by 3 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{5}{3} \][/tex]
3. Substitute [tex]\(x = \frac{5}{3}\)[/tex] back into the function [tex]\(f\left(\frac{3 x-1}{2}\right)=6 x+1\)[/tex] to find [tex]\( f(2) \)[/tex]:
- The given function can be rewritten with [tex]\(x = \frac{5}{3}\)[/tex]:
[tex]\[ f\left(2\right) = 6 \left(\frac{5}{3}\right) + 1 \][/tex]
- Simplify inside the parenthesis:
[tex]\[ f(2) = 2 \times 5 + 1 \][/tex]
[tex]\[ f(2) = 10 + 1 \][/tex]
[tex]\[ f(2) = 11 \][/tex]
Hence, the value of [tex]\( f(2) \)[/tex] is [tex]\( 11 \)[/tex].
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.