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Chapter 4: Problem 41

\(y=\left\\{\begin{array}{ll}{-x^{2}-2 x+4,} & {x \leq 1} \\ {-x^{2}+6 x-4,} & {x > 1}\end{array}\right.\)

Short Answer

Expert verified
The output y is obtained by substitifying the value of x in the appropriate equation and simplifying the result. The appropriate equation is determined by whether x is less than or equal to 1, or greater than 1.

Step by step solution

01

Apply Appropriate Equation

For a specific input value of x, first determine which equation to use. If x is less than or equal to 1, use the first equation \( -x^{2} -2x + 4 \). If x is greater than 1, use the second equation \( -x^{2} +6x - 4 \). The result y is directly calculated by substituting the given value of x in the chosen equation.
02

Simplification

Simplify the equation by performing the calculations in the right order (PEMDAS/BODMAS - parentheses/brackets, exponents/orders, multiplication and division, addition and subtraction).
03

Final Result

The result of the simplification is the output y of the function for the given input x.

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Most popular questions from this chapter

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