(1) 상수 a \displaystyle a a b \displaystyle b b c \displaystyle c c
+5점 · a = − 1 \displaystyle a=-1 a = − 1 b = 0 \displaystyle b=0 b = 0 c = 1 \displaystyle c=1 c = 1 ▶ f ( x ) = a x + b + c \displaystyle f(x)=\sqrt{ax+b}+c f ( x ) = a x + b + c { x ∣ x ≤ 0 } \displaystyle \{x\mid x\le0\} { x ∣ x ≤ 0 } { y ∣ y ≥ 1 } \displaystyle \{y\mid y\ge1\} { y ∣ y ≥ 1 } f ( x ) = a x + 1 \displaystyle f(x)=\sqrt{ax}+1 f ( x ) = a x + 1 f ( x ) = a x + 1 \displaystyle f(x)=\sqrt{ax}+1 f ( x ) = a x + 1 ( − 4 , 3 ) \displaystyle (-4,3) ( − 4 , 3 ) a = − 1 \displaystyle a=-1 a = − 1 f ( x ) = − x + 1 \displaystyle f(x)=\sqrt{-x}+1 f ( x ) = − x + 1 a = − 1 \displaystyle a=-1 a = − 1 b = 0 \displaystyle b=0 b = 0 c = 1 \displaystyle c=1 c = 1
(2) 무리함수 y = f ( x ) \displaystyle y=f(x) y = f ( x ) y = f − 1 ( x ) \displaystyle y=f^{-1}(x) y = f − 1 ( x ) y = f − 1 ( x ) \displaystyle y=f^{-1}(x) y = f − 1 ( x )
+3점 · 역함수 y = − ( x − 1 ) 2 \displaystyle y=-(x-1)^2 y = − ( x − 1 ) 2 +2점 · 정의역 { x ∣ x ≥ 1 } \displaystyle \{x\mid x\ge1\} { x ∣ x ≥ 1 } ▶ f ( x ) = − x + 1 \displaystyle f(x)=\sqrt{-x}+1 f ( x ) = − x + 1 x = − y + 1 \displaystyle x=\sqrt{-y}+1 x = − y + 1 y = − ( x − 1 ) 2 ( x ≥ 1 ) \displaystyle y=-(x-1)^2\quad(x\ge1) y = − ( x − 1 ) 2 ( x ≥ 1 ) 이다. 또한 역함수의 정의역은 { x ∣ x ≥ 1 } \displaystyle \{x\mid x\ge1\} { x ∣ x ≥ 1 }
(3) 무리함수 y = f ( x ) \displaystyle y=f(x) y = f ( x ) y \displaystyle y y y = 3 \displaystyle y=3 y = 3 S \displaystyle S S y = f − 1 ( x ) \displaystyle y=f^{-1}(x) y = f − 1 ( x ) S \displaystyle S S [보기] S = ∫ α β ∣ f − 1 ( x ) ∣ d x \displaystyle S=\int_\alpha^\beta|f^{-1}(x)|\,dx S = ∫ α β ∣ f − 1 ( x ) ∣ d x α \displaystyle \alpha α β \displaystyle \beta β 이를 활용하여 α \displaystyle \alpha α β \displaystyle \beta β S \displaystyle S S y = f − 1 ( x ) \displaystyle y=f^{-1}(x) y = f − 1 ( x )
+5점 · α = 1 \displaystyle \alpha=1 α = 1 β = 3 \displaystyle \beta=3 β = 3 +5점 · S = ∫ 1 3 ∣ f − 1 ( x ) ∣ d x = 8 3 \displaystyle S=\int_1^3|f^{-1}(x)|\,dx=\frac83 S = ∫ 1 3 ∣ f − 1 ( x ) ∣ d x = 3 8 ▶ 그림에서 무리함수 y = f ( x ) \displaystyle y=f(x) y = f ( x ) y \displaystyle y y y = 3 \displaystyle y=3 y = 3 y \displaystyle y y 1 ≤ y ≤ 3 \displaystyle 1\le y\le3 1 ≤ y ≤ 3 따라서 역함수 y = f − 1 ( x ) \displaystyle y=f^{-1}(x) y = f − 1 ( x ) x \displaystyle x x x = 3 \displaystyle x=3 x = 3 x \displaystyle x x 1 ≤ x ≤ 3 \displaystyle 1\le x\le3 1 ≤ x ≤ 3 α = 1 \displaystyle \alpha=1 α = 1 β = 3 \displaystyle \beta=3 β = 3 S \displaystyle S S S = ∫ 1 3 ∣ f − 1 ( x ) ∣ d x = ∫ 1 3 ∣ − ( x − 1 ) 2 ∣ d x = 8 3 \displaystyle S=\int_1^3|f^{-1}(x)|\,dx=\int_1^3|-(x-1)^2|\,dx=\frac83 S = ∫ 1 3 ∣ f − 1 ( x ) ∣ d x = ∫ 1 3 ∣ − ( x − 1 ) 2 ∣ d x = 3 8 이다.
수리논술, 배움에서 논증의 완성까지.