Show that f-1-1- R given by fx-xx-2 is one-one- Find the inverse of the function f-1-1-

The correct option is A g(y)=(2y1 y) ⇒ f(x)=xx+2 y=xx+2 xy+2y=x xy x= 2y 2y=x xy 2y=x(1 y) X=2y1 y f^ 1(x)=2y1 y ...

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Standard XII

Mathematics

Algebra of Derivatives

Show that f...

Question

Show that $f : [- 1, 1] \to R$ given by $f (x) = \frac{x}{(x + 2)}$ is one-one. Find the inverse of the function $f : [- 1, 1]$

g (y) = (\frac{2 y}{1 - y})

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g (y) = (\frac{y}{1 - y})

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g (y) = (\frac{2 y}{2 - y})

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g (y) = (\frac{y}{2 - y})

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Solution

The correct option is A $g (y) = (\frac{2 y}{1 - y})$
$\Rightarrow f (x) = \frac{x}{x + 2}$
$y = \frac{x}{x + 2}$
$x y + 2 y = x$
$x y - x = - 2 y$
$2 y = x - x y$
$2 y = x (1 - y)$
$X = \frac{2 y}{1 - y}$
$f^{- 1} (x) = \frac{2 y}{1 - y}$

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Show that f:[−1,1]→R given by f(x)=x(x+2) is one-one. Find the inverse of the function f:[−1,1]

The correct option is A g(y)=(2y1−y)⇒f(x)=xx+2y=xx+2xy+2y=xxy−x=−2y2y=x−xy2y=x(1−y)X=2y1−yf−1(x)=2y1−y

Show that $f : [- 1, 1] \to R$ given by $f (x) = \frac{x}{(x + 2)}$ is one-one. Find the inverse of the function $f : [- 1, 1]$

The correct option is A $g (y) = (\frac{2 y}{1 - y})$
$\Rightarrow f (x) = \frac{x}{x + 2}$
$y = \frac{x}{x + 2}$
$x y + 2 y = x$
$x y - x = - 2 y$
$2 y = x - x y$
$2 y = x (1 - y)$
$X = \frac{2 y}{1 - y}$
$f^{- 1} (x) = \frac{2 y}{1 - y}$