Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
To find the value of [tex]\( f(19) \)[/tex] for the function [tex]\( f(x) = \frac{3}{x+2} - \sqrt{x - 3} \)[/tex], we start by substituting [tex]\( x = 19 \)[/tex] into the given function:
[tex]\[ f(x) = \frac{3}{x+2} - \sqrt{x-3} \][/tex]
Substituting [tex]\( x = 19 \)[/tex]:
[tex]\[ f(19) = \frac{3}{19+2} - \sqrt{19-3} \][/tex]
First, simplify the terms inside the function:
1. Calculate [tex]\( 19 + 2 \)[/tex]:
[tex]\[ 19 + 2 = 21 \][/tex]
2. Calculate [tex]\( 19 - 3 \)[/tex]:
[tex]\[ 19 - 3 = 16 \][/tex]
Next, substitute these simplified values back into the function:
[tex]\[ f(19) = \frac{3}{21} - \sqrt{16} \][/tex]
Now, compute each part separately:
1. Calculate [tex]\( \frac{3}{21} \)[/tex]:
[tex]\[ \frac{3}{21} = \frac{1}{7} \][/tex]
2. Calculate [tex]\( \sqrt{16} \)[/tex]:
[tex]\[ \sqrt{16} = 4 \][/tex]
Therefore, the function becomes:
[tex]\[ f(19) = \frac{1}{7} - 4 \][/tex]
Converting [tex]\( \frac{1}{7} \)[/tex] into a decimal for simplicity:
[tex]\[ \frac{1}{7} \approx 0.142857 \][/tex]
So, substituting back:
[tex]\[ f(19) = 0.142857 - 4 \][/tex]
Finally, subtract 4 from the decimal value:
[tex]\[ 0.142857 - 4 = -3.857142857142857 \][/tex]
Thus, the complete statement is:
[tex]\[ f(19) = -3.857142857142857 \][/tex]
[tex]\[ f(x) = \frac{3}{x+2} - \sqrt{x-3} \][/tex]
Substituting [tex]\( x = 19 \)[/tex]:
[tex]\[ f(19) = \frac{3}{19+2} - \sqrt{19-3} \][/tex]
First, simplify the terms inside the function:
1. Calculate [tex]\( 19 + 2 \)[/tex]:
[tex]\[ 19 + 2 = 21 \][/tex]
2. Calculate [tex]\( 19 - 3 \)[/tex]:
[tex]\[ 19 - 3 = 16 \][/tex]
Next, substitute these simplified values back into the function:
[tex]\[ f(19) = \frac{3}{21} - \sqrt{16} \][/tex]
Now, compute each part separately:
1. Calculate [tex]\( \frac{3}{21} \)[/tex]:
[tex]\[ \frac{3}{21} = \frac{1}{7} \][/tex]
2. Calculate [tex]\( \sqrt{16} \)[/tex]:
[tex]\[ \sqrt{16} = 4 \][/tex]
Therefore, the function becomes:
[tex]\[ f(19) = \frac{1}{7} - 4 \][/tex]
Converting [tex]\( \frac{1}{7} \)[/tex] into a decimal for simplicity:
[tex]\[ \frac{1}{7} \approx 0.142857 \][/tex]
So, substituting back:
[tex]\[ f(19) = 0.142857 - 4 \][/tex]
Finally, subtract 4 from the decimal value:
[tex]\[ 0.142857 - 4 = -3.857142857142857 \][/tex]
Thus, the complete statement is:
[tex]\[ f(19) = -3.857142857142857 \][/tex]
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.