Suppose that the functions \( h \) and \( g \) are defined as follows. \[ \begin{array}{l}h(x)=3 x^{2}-4 \\ g(x)=8 x-3\end{array} \] (a) Find \( \left(\frac{h}{g}\right)(-1) \). (b) Find all values that are NOT in the domain of \( \frac{h}{g} \). If there is more than one value, separate them with commas. (a) \( \left(\frac{h}{g}\right)(-1)=\square \) (b) Value(s) that are NOT in the domain of \( \frac{h}{g}: \square \)

Complete the square to write \( y=2 x^{2}+12 x-7 \) in graphing form. Then determine the vertex and the intercepts of the parabola. 1

\( f(x)=5 x+6 ; g(x)=3 x-2 \) (h) Find \( \left(\frac{1}{g}\right)(1) \).

QUESTION 12 If \( 2^{x} 5^{y}=16 \times 125 \), where \( x \) and \( y \) are positive integers, determine \( x-y \) :

Câu 01: (a) Cho hàm số \( f(x)=a x^{2}-\sqrt{2} \). Tìm \( a \) biết rằng \( (f \circ f)(\sqrt{2})=-\sqrt{2} \). (b) Tìm \( m \) để hàm số \( y=\sqrt{2 x-3 m+4}-\frac{x-m}{x+m-1} \) xác định với mọi \( x>0 \).

Simplify he following fully: \( \frac{3^{3+1}-3^{-1}}{23^{x}} \) \( \frac{3^{x} \cdot 3^{1}-3^{x} \cdot 3^{-1}}{2 \cdot 3^{x}} \frac{3^{x}\left(1-\frac{1}{3}\right)}{23^{x}} \)