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3 years ago

Need help with 2 and 4 ASAP Inverses...

Mathematics

1 answer:

Drupady [299]3 years ago

4 0

h(x) = 1/(x - 1)

Replace h(x) with y.

y = 1/(x - 1)

Swap x and y.

x = 1/(y - 1)

Solve for y.

Multiply both sides by (y - 1)

x(y - 1) = 1

Distributive property.

xy - x = 1

Add x to both sides.

xy = 1 + x

Divide both sides by x.

y = 1/x + 1

Replace y with h^-1(x)

H^-1(x) = 1/x + 1 is the inverse function for question 2.

h(x) = 4/(x + 2)

Replace h(x) with y.

y = 4/(x + 2)

Swap y and x.

x = 4/(y + 2)

Solve for y.

Multiply both sides by y + 2.

x(y + 2) = 4

Distributive property.

xy + 2x = 4

Subtract both sides by 2x.

xy = 4 - 2x

Divide both sides by x.

y = 4/x - 2

Replace y with h^-1(x)

H^-1(x) = 4/x - 2 is the inverse function for question 4.

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The variance method is as follows.

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14 = \frac{29}{3}+ \frac{1}{3}m^2 - \frac{1}{9}(49 + 14m + m^2) \\ \\
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$m = \displaystyle\frac{-b \pm \sqrt{b^2 -4ac}}{2a} \\
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m = \frac{\frac{14}{9} \pm \sqrt{ \frac{900}{81} } }{\frac{4}{9} } \\
m = \frac{\frac{14}{9} \pm \sqrt{ \frac{100}{9} } }{\frac{4}{9} } \\
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-4 doesnt' work as it is not a positive integer

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