Precalculus (6th Edition)

(a) $f(x)=3x^2+x+2$ (b) $(3)=32$
(a) function notation. Solve for $y$: \begin{array}{ccc} &y-3x^2&=&2+x \\&y-3x^2+3x^2&= &2+x+3x^2 \\&y&=&3x^2+x+2 \end{array} Let $y=f(x)$. The equation becomes: $$f(x)=3x^2+x+2$$ (b) To find $f(3)$, substitute $3$ to $x$ in $f(x)$ to obtain: $f(x)= 3x^2+x+2 \\f(3) = 3(3^2)+3+2 \\f(3)=3(9)+3+2 \\f(3)=27+3+2 \\f(3)=32$