Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
To solve [tex]\( f(x) = \sin \sqrt{6x^4 - 8x - 3} \)[/tex], we need to evaluate the given function step-by-step. Let's break down this complex function into more manageable parts.
1. Examine the Inner Expression:
- The expression inside the sine function is [tex]\( \sqrt{6x^4 - 8x - 3} \)[/tex].
2. Simplify the Inner Expression:
- Calculate the term [tex]\( 6x^4 \)[/tex]. This means raising [tex]\( x \)[/tex] to the fourth power and multiplying the result by 6.
- Calculate the term [tex]\( -8x \)[/tex]. This means multiplying [tex]\( x \)[/tex] by -8.
- Subtract 3 from the sum of these two terms.
3. Form the Argument of the Sine Function:
- Take the square root of the expression [tex]\( 6x^4 - 8x - 3 \)[/tex]. This is done by power [tex]\( \frac{1}{2} \)[/tex].
4. Apply the Sine Function:
- Finally, apply the sine function to the result obtained from step 3.
Thus, for a given value of [tex]\( x \)[/tex], the step-by-step computation would look like:
- Compute [tex]\( 6x^4 \)[/tex].
- Compute [tex]\( -8x \)[/tex].
- Sum these results and subtract 3.
- Take the square root of the outcome.
- Apply the sine function to this square root.
Therefore, the function [tex]\( f(x) \)[/tex] can be expressed as:
[tex]\[ f(x) = \sin \left( \sqrt{6x^4 - 8x - 3} \right) \][/tex]
This is the detailed step-by-step solution for the function [tex]\( f(x) \)[/tex].
1. Examine the Inner Expression:
- The expression inside the sine function is [tex]\( \sqrt{6x^4 - 8x - 3} \)[/tex].
2. Simplify the Inner Expression:
- Calculate the term [tex]\( 6x^4 \)[/tex]. This means raising [tex]\( x \)[/tex] to the fourth power and multiplying the result by 6.
- Calculate the term [tex]\( -8x \)[/tex]. This means multiplying [tex]\( x \)[/tex] by -8.
- Subtract 3 from the sum of these two terms.
3. Form the Argument of the Sine Function:
- Take the square root of the expression [tex]\( 6x^4 - 8x - 3 \)[/tex]. This is done by power [tex]\( \frac{1}{2} \)[/tex].
4. Apply the Sine Function:
- Finally, apply the sine function to the result obtained from step 3.
Thus, for a given value of [tex]\( x \)[/tex], the step-by-step computation would look like:
- Compute [tex]\( 6x^4 \)[/tex].
- Compute [tex]\( -8x \)[/tex].
- Sum these results and subtract 3.
- Take the square root of the outcome.
- Apply the sine function to this square root.
Therefore, the function [tex]\( f(x) \)[/tex] can be expressed as:
[tex]\[ f(x) = \sin \left( \sqrt{6x^4 - 8x - 3} \right) \][/tex]
This is the detailed step-by-step solution for the function [tex]\( f(x) \)[/tex].
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.