QuestionTwo functions are shown below.
What is the -value when ?
Studdy Solution
STEP 1
1. We are given two functions: and .
2. We need to find the -value where .
STEP 2
1. Set the two functions equal to each other.
2. Solve the resulting equation for .
3. Substitute the value(s) of back into either function to find the corresponding -value(s).
STEP 3
Set the two functions equal to each other:
STEP 4
Consider the absolute value expression . This expression can be split into two cases:
Case 1: (i.e., )
Case 2: (i.e., )
STEP 5
Solve Case 1 ():
Multiply through by 2 to eliminate the fraction:
Rearrange the equation:
STEP 6
Solve Case 2 ():
Multiply through by 2 to eliminate the fraction:
Rearrange the equation:
STEP 7
Solve the cubic equations obtained from both cases.
For Case 1:
For Case 2:
These equations may need numerical methods or graphing to find solutions.
STEP 8
Assume numerical solutions or graphing gives us the -values where the equations hold true. Let's assume the solutions are .
Substitute these -values back into either or to find the corresponding -values.
The -value(s) when are the result of substituting the solution -values back into either function.
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