Find the Set of Values of \( x \)
Question:
Find the set of values of \(x\) for which the functions
\[ f(x)=3x^2-1 \]
and
\[ g(x)=x+3 \]
are equal.
Solution:
For equal functions,
\[ f(x)=g(x) \]
Therefore,
\[ 3x^2-1=x+3 \]
\[ 3x^2-x-4=0 \]
Factorizing,
\[ 3x^2-4x+3x-4=0 \]
\[ (x- \tfrac{4}{3})(3x+3)=0 \]
\[ (x+1)(3x-4)=0 \]
Hence,
\[ x=-1 \quad \text{or} \quad x=\frac43 \]
Therefore, the set of values is
\[ \boxed{\left\{-1,\frac43\right\}} \]