Question #N452
The function \(f(x)\) is defined by \(f(x)=x^2+3x-4\). For what value of \(x\) does \(f(x)=10\)?
A. -7
B. -3
C. 1
D. 4
Correct Answer is: C
To solve for \(x\), we set the function equal to 10: \(x^2+3x-4=10\). Subtracting 10 from both sides gives us \(x^2+3x-14=0\). We can factor this quadratic equation as \((x+7)(x-2)=0\). Setting each factor equal to zero gives us \(x+7=0\) or \(x-2=0\). Solving for \(x\) in each equation gives us \(x=-7\) or \(x=2\). Of these, only 1 is given as a choice. Therefore, the value of \(x\) for which \(f(x)=10\) is \(x=1\).