Solving Polynomial Functions: Find x in 0<|x|≤1/2

Thread starter mtayab1994
Start date Nov 1, 2011
Tags

Function Polynomial

In summary, to solve polynomial functions to find x, you can use the substitution method, factoring method, or quadratic formula. "0<|x|≤1/2" in this context means that x is greater than 0 and less than or equal to 1/2. The substitution method involves replacing the variable with a known value, the factoring method is useful for polynomials with multiple terms, and the solution is valid if it satisfies the equation and falls within the specified range of values.

Nov 1, 2011

mtayab1994

Homework Statement

f:ℝ→ℝ
x:→sqrt(x^2+1)-lxl

Homework Equations

calculate f^-1(]0,1])

The Attempt at a Solution

well i chose a y from ]0,1] and tried to find an x that solves the problem like the following.

0<sqrt(x^2+1)-lxl≤1

at the end i got the following: 0<lxl≤1/2 is my work correct?

Physics news on Phys.org

Nov 1, 2011

micromass

Staff Emeritus

Science Advisor

Homework Helper

Insights Author

No it is not correct. What is your work??

Related to Solving Polynomial Functions: Find x in 0<|x|≤1/2

1. How do you solve polynomial functions to find x?

To solve polynomial functions to find x, you can use the substitution method, the factoring method, or the quadratic formula. The method used will depend on the type of polynomial and the given information.

2. What does "0<|x|≤1/2" mean in this context?

In this context, "0<|x|≤1/2" means that the absolute value of x is greater than 0 and less than or equal to 1/2. This is used to specify the range of values that x can take in the polynomial function.

3. Can you explain the substitution method for solving polynomial functions?

The substitution method involves replacing the variable in the polynomial function with a known value and then solving for the remaining variable. This method is useful when there is a single variable in the polynomial function.

4. When should I use the factoring method to solve polynomial functions?

The factoring method is most useful when the polynomial function can be written as a product of two or more simpler expressions. This method is helpful when the polynomial has multiple terms and can also be used to find the zeros of the function.

5. How do I know if the solution to a polynomial function is valid?

The solution to a polynomial function is valid if it satisfies the given equation and falls within the specified range of values for the variable. You can check the validity of the solution by substituting it back into the original equation and ensuring that it equals the given value.