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rewona [7]
3 years ago
13

What is the inverse of the function

id="TexFormula1" title="a(x) = \frac{1}{x} - 2" alt="a(x) = \frac{1}{x} - 2" align="absmiddle" class="latex-formula">
Mathematics
2 answers:
Verdich [7]3 years ago
6 0

a(x) = 1/x - 2

or

y = 1/x - 2

Switch x and y to find the inverse function

x = 1/y - 2

1/y = x + 2

y = 1 / (x + 2)


Answer

a^-1(x) = 1 / (x + 2)

larisa [96]3 years ago
4 0

To find the inverse, swap the x's and y's and solve for y. <em>Remember that a(x) represents y</em>

y = \frac{1}{x} - 2 <em>given</em>

x = \frac{1}{y} - 2 <em>x's and y's swapped</em>

x + 2 = \frac{1}{y} <em>added 2 to both sides</em>

y(x + 2) = 1 <em>multiplied y on both sides</em>

y = \frac{1}{x + 2} divided (x + 2) on both sides

Answer: a^{-1} (x) = \frac{1}{x + 2}

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