If $s(x) = 2 - X^2$ And $t(x) = 3x$, Which Value Is Equivalent To $(s \circ T)(-7$\]?A. $-439$ B. $-141$ C. $153$ D. $443$

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Introduction

In mathematics, a composition of functions is a way of combining two or more functions to create a new function. This is a fundamental concept in algebra and calculus, and it has numerous applications in various fields, including physics, engineering, and economics. In this article, we will explore the concept of composition of functions, and we will use the given functions s(x)=2−x2s(x) = 2 - x^2 and t(x)=3xt(x) = 3x to find the value of (s∘t)(−7)(s \circ t)(-7).

What is a Composition of Functions?

A composition of functions is a way of combining two or more functions to create a new function. This is done by plugging one function into another function. For example, if we have two functions f(x)f(x) and g(x)g(x), then the composition of ff and gg is denoted by f∘gf \circ g and is defined as:

(f∘g)(x)=f(g(x))(f \circ g)(x) = f(g(x))

Composition of Functions: A Step-by-Step Guide

To find the value of (s∘t)(−7)(s \circ t)(-7), we need to follow these steps:

  1. Evaluate the inner function: First, we need to evaluate the inner function t(x)=3xt(x) = 3x at x=−7x = -7. This means we need to plug −7-7 into the function t(x)t(x) and simplify.

t(−7)=3(−7)=−21t(-7) = 3(-7) = -21

  1. Plug the result into the outer function: Now that we have the value of t(−7)t(-7), we can plug it into the outer function s(x)=2−x2s(x) = 2 - x^2. This means we need to replace xx in the function s(x)s(x) with −21-21.

s(−21)=2−(−21)2s(-21) = 2 - (-21)^2

  1. Simplify the expression: Now that we have the expression s(−21)=2−(−21)2s(-21) = 2 - (-21)^2, we can simplify it by evaluating the exponent and then subtracting the result from 2.

s(−21)=2−441s(-21) = 2 - 441

  1. Evaluate the final expression: Finally, we can evaluate the final expression s(−21)=2−441s(-21) = 2 - 441 by subtracting 441 from 2.

s(−21)=−439s(-21) = -439

Conclusion

In this article, we explored the concept of composition of functions and used the given functions s(x)=2−x2s(x) = 2 - x^2 and t(x)=3xt(x) = 3x to find the value of (s∘t)(−7)(s \circ t)(-7). We followed a step-by-step guide to evaluate the inner function, plug the result into the outer function, simplify the expression, and finally evaluate the final expression. The value of (s∘t)(−7)(s \circ t)(-7) is equivalent to −439-439.

Answer

The correct answer is A. −439-439.

References

  • [1] "Composition of Functions" by Khan Academy
  • [2] "Composition of Functions" by Math Open Reference
  • [3] "Composition of Functions" by Wolfram MathWorld
    Composition of Functions: A Q&A Guide =====================================

Introduction

In our previous article, we explored the concept of composition of functions and used the given functions s(x)=2−x2s(x) = 2 - x^2 and t(x)=3xt(x) = 3x to find the value of (s∘t)(−7)(s \circ t)(-7). In this article, we will answer some frequently asked questions about composition of functions.

Q&A

Q: What is the difference between a composition of functions and a product of functions?

A: A composition of functions is a way of combining two or more functions to create a new function, whereas a product of functions is a way of multiplying two or more functions together.

Q: How do I evaluate a composition of functions?

A: To evaluate a composition of functions, you need to follow these steps:

  1. Evaluate the inner function at the given input.
  2. Plug the result into the outer function.
  3. Simplify the expression.
  4. Evaluate the final expression.

Q: What is the order of operations for a composition of functions?

A: The order of operations for a composition of functions is the same as the order of operations for a single function. You need to follow the order of operations (PEMDAS) to evaluate the expression.

Q: Can I use a composition of functions to solve a system of equations?

A: Yes, you can use a composition of functions to solve a system of equations. By combining two or more functions, you can create a new function that represents the solution to the system of equations.

Q: How do I determine if a composition of functions is one-to-one?

A: To determine if a composition of functions is one-to-one, you need to check if the inner function is one-to-one. If the inner function is one-to-one, then the composition of functions is also one-to-one.

Q: Can I use a composition of functions to find the inverse of a function?

A: Yes, you can use a composition of functions to find the inverse of a function. By combining two or more functions, you can create a new function that represents the inverse of the original function.

Q: What is the difference between a composition of functions and a function of a function?

A: A composition of functions is a way of combining two or more functions to create a new function, whereas a function of a function is a way of plugging one function into another function.

Q: Can I use a composition of functions to solve a differential equation?

A: Yes, you can use a composition of functions to solve a differential equation. By combining two or more functions, you can create a new function that represents the solution to the differential equation.

Conclusion

In this article, we answered some frequently asked questions about composition of functions. We covered topics such as the difference between a composition of functions and a product of functions, how to evaluate a composition of functions, and how to determine if a composition of functions is one-to-one. We also discussed how to use a composition of functions to solve a system of equations, find the inverse of a function, and solve a differential equation.

References

  • [1] "Composition of Functions" by Khan Academy
  • [2] "Composition of Functions" by Math Open Reference
  • [3] "Composition of Functions" by Wolfram MathWorld

Additional Resources

  • [1] "Composition of Functions" by MIT OpenCourseWare
  • [2] "Composition of Functions" by Stanford University
  • [3] "Composition of Functions" by University of California, Berkeley