Question 1
(a) Sketch \( y = x^2 \).
(b) Find the domain that \( y=x^2 \) is restricted to a monotonic increasing curve..
\( x \gt 0 \)
(c) Find the inverse of \( y = x^2 \).
\( \begin{align} y^2 &= x \\ y &= \pm \sqrt{x} \\ y &= \sqrt{x} \\ y^{-1} &= \sqrt{x}, \ x \ge 0 \end{align} \)
Question 2
(a) Sketch \( y = x^2-2x \).
(b) Find the domain that \( y = x^2-2x \) is restricted to a monotonic decreasing curve.
\( x \lt 1 \)
(c) Find the inverse of \( y = x^2-2x \).
\( \begin{align} y^2-2x &= x \\ u^2-2y+1 &= x+2 \\ (y-1)^2 &= x+2 \\ y-1 &= \pm\sqrt{x+1} \\ y &= 1 \pm \sqrt{x+2} \\ y^{-1} &= 1-\sqrt{x+1} \end{align} \)
(d) Find the domain of \( y^{-1} \).
\( x \gt -1 \)
(e) Find the range of \( y^{-1} \).
\( y \lt 1 \)
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