Suppose that the functions \( g \) and \( f \) are defined as follows. \( g(x)=x-5 \) \( f(x)=(x+6)(x-6) \) (a) Find \( \left(\frac{g}{f}\right)(-2) \). (b) Find all values that are NOT in the domain of \( \frac{g}{f} \). If there is more than one value, separate them with commas. (a) \( \left(\frac{g}{f}\right)(-2)= \) fil (b) Value(s) that are NOT in the domain of \( \frac{g}{f}: \square \)

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

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 \( x>0 \).

How much pure acid should be mixed with 2 gallons of a \( 50 \% \) acid solution to get an \( 80 \% \) acid solution?

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

Câu 03: (a) Rût gơn biểu thực \[ \left(\frac{1-x}{x^{2}+x^{3}-x^{4}}-\frac{x^{2}+x+2}{x^{5}-x^{3}-2 x^{2}-x}\right):\left(\frac{1+x^{4}}{x^{3}+x^{4}+x^{5}}-\frac{1-x+x^{2}}{x}\right) \] (b) Phân tích phân thức \( \frac{1}{(x-1)(x-2)(x-3)(x-4)} \) thành tổng các phân thức dơn giản.