Chapter 1 Linear Systems 1. Solve each linear system. For each system, explain why you chose the method that you used. Check each solution. a) \( x+2 y=3 \) \( 3 x-y=1 \)

Solve for \( x \) : \( 3^{x}=32 \) \( x= \) You may enter the exact value or round to 4 decimal places.

*a). Given that \( f(x)=2 x+1 \) and \( g(x)=x^{2}-2 \), obtain (i) \( f \circ g(0) \) (ii) \( \left(g \circ f^{-1}(-2)\right. \)

2 Find, in the form \( y=a x^{2}+b x+c \), the equation of the quadratic whose graph: a touches the \( x \)-axis at 4 and passes through \( (2,12) \) b has vertex \( (-4,1) \) and passes through \( (1,11) \)

1. \( \frac{x}{3}=\frac{2}{3} \) \( x=3(2)(3) \)

Show that \( (f \cdot g)^{-1}=g^{-1} \cdot f^{-1} \) given that \( f(x)=\frac{x-1}{x+2} \) \( g(x)=\frac{5}{x-5} \)