Problem 98

Question

Find \(f(-x)-f(x)\) for the given function \(f\) Then simplify the expression. $$f(x)=x^{2}-3 x+7$$

Step-by-Step Solution

Verified
Answer
The final result for \(f(-x) - f(x)\) is \(6x\)
1Step 1: Compute \(f(-x)\)
To compute \(f(-x)\), replace each instance of \(x\) in the given function with \(-x\). The resultant function becomes \(f(-x)= (-x)^{2}-3(-x)+7\)
2Step 2: Simplify \(f(-x)\)
Simplify the above equation to get \(f(-x) = x^{2}+3x+7\)
3Step 3: Compute \(f(-x)-f(x)\)
Subtract \(f(x)\) from \(f(-x)\). That is calculate \(f(-x)-f(x) = (x^{2}+3x+7) - (x^{2}-3x+7)\)
4Step 4: Simplify the Expression
By simplifying \(f(-x)-f(x)\), the result will be \(6x\)