Combination of Functions

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January 14th 2008, 04:23 PM
Macleef

Combination of Functions

Find the inverse of each function.

g)

$y = \frac {x + 5}{x -5}$

Where did I go wrong?

$x = \frac {y + 5}{y - 5}$

$x(y - 5) = y + 5$

$x(y - 5) -5 = y$

$xy - 5x - 5 = y$

$-5x - 5 = y - xy$

$-5x - 5 = y(1 - x)$

$\frac {-5x - 5}{1 - x} = y$

$\frac {-5(x + 1)}{1 - x} = y$

Even if I move it to the right side. . .I get a different answer. . .

y = $\frac {5(x - 1)}{x - 1}$

Correct answer is. . .

$\frac {5(x + 1)}{x - 1}$

h)

$y = \frac {1}{x^2}$

Is my answer correct?

$x(y^2) = 1$

$y^2 = \frac {1}{x}$

$y = \sqrt{\frac {1}{x}}$
January 14th 2008, 08:13 PM
CaptainBlack

Quote:

Originally Posted by Macleef

Find the inverse of each function.

g)

$y = \frac {x + 5}{x -5}$

Where did I go wrong?

$x = \frac {y + 5}{y - 5}$

$x(y - 5) = y + 5$

$x(y - 5) -5 = y$

$xy - 5x - 5 = y$

$-5x - 5 = y - xy$

$-5x - 5 = y(1 - x)$

$\frac {-5x - 5}{1 - x} = y$

$\frac {-5(x + 1)}{1 - x} = y$

Even if I move it to the right side. . .I get a different answer. . .

y = $\frac {5(x - 1)}{x - 1}$

Correct answer is. . .

$\frac {5(x + 1)}{x - 1}$

You have:

$\frac {-5(x + 1)}{1 - x} = y$

or:

$y=\frac {-5(x + 1)}{1 - x}=\frac{5(x+1)}{(x-1)}$

(that is multiply top and bottom of the middle term side by $-1$ to get the right most term, which is the desired answer)
January 14th 2008, 08:14 PM
CaptainBlack

Quote:

Originally Posted by Macleef

h)

$y = \frac {1}{x^2}$

Is my answer correct?

$x(y^2) = 1$

$y^2 = \frac {1}{x}$

$y = \sqrt{\frac {1}{x}}$

Subject to the restriction that $x > 0$ yes except that you have reversed the meaning of $x$ and $y$ .

$y(x^2) = 1$

$x^2 = \frac {1}{y}$

$x = \sqrt{\frac {1}{y}}$

when $y > 0$

RonL