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人気のある代数 >

solvefor x,f^{-1}(x)=(x+3)^2

解

解く

x, f^{- 1} (x) = (x + 3)^{2}

解

x = \frac{- 6 f + 1 + 1 - 12 f}{2 f}, x = \frac{- 6 f + 1 - 1 - 12 f}{2 f}

解答ステップ

f^{- 1} (x) = (x + 3)^{2}

拡張

(x + 3)^{2} : x^{2} + 6 x + 9

\frac{x}{f} = x^{2} + 6 x + 9

辺を交換する

x^{2} + 6 x + 9 = \frac{x}{f}

\frac{x}{f}

を左側に移動します

x^{2} + 6 x + 9 - \frac{x}{f} = 0

標準的な形式で書く

a x^{2} + b x + c = 0

x^{2} + (6 - \frac{1}{f}) x + 9 = 0

解くとthe二次式

x_{1, 2} = \frac{- ( 6 - \frac{1}{f} ) \pm ( 6 - \frac{1}{f} ) ^{2} - 4 \cdot 1 \cdot 9}{2 \cdot 1}

簡素化

(6 - \frac{1}{f})^{2} - 4 \cdot 1 \cdot 9 : \frac{1 - 12 f}{f}

x_{1, 2} = \frac{- ( 6 - \frac{1}{f} ) \pm \frac{1 - 12 f}{f}}{2 \cdot 1}

解を分離する

x_{1} = \frac{- ( 6 - \frac{1}{f} ) + \frac{1 - 12 f}{f}}{2 \cdot 1}, x_{2} = \frac{- ( 6 - \frac{1}{f} ) - \frac{1 - 12 f}{f}}{2 \cdot 1}

x = \frac{- ( 6 - \frac{1}{f} ) + \frac{1 - 12 f}{f}}{2 \cdot 1} : \frac{- 6 f + 1 + 1 - 12 f}{2 f}

x = \frac{- ( 6 - \frac{1}{f} ) - \frac{1 - 12 f}{f}}{2 \cdot 1} : \frac{- 6 f + 1 - 1 - 12 f}{2 f}

二次equationの解:

x = \frac{- 6 f + 1 + 1 - 12 f}{2 f}, x = \frac{- 6 f + 1 - 1 - 12 f}{2 f}

グラフ

人気の例

solvefor x,x^2+x+4=0

so l v e f or x, x^{2} + x + 4 = 0

3 x^{2} + 8 x = 2

completesquare 3x^2-4x+5

co m pl e t es q u a re 3 x^{2} - 4 x + 5

solvefor x,x(1-x)y^n+(3/2-2x)y^1+2y=0

so l v e f or x, x (1 - x) y^{n} + (\frac{3}{2} - 2 x) y^{1} + 2 y = 0

x^{2} - x = x - 1