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2 years ago

What is the inverse of the function f(x) = 1/9x+ 2?

Mathematics

1 answer:

hichkok12 [17]2 years ago

4 0

Answer:

$f^{-1}(x) = 9x -18.$

Step-by-step explanation:

$y=f(x)=\dfrac 19 x +2\\\\\text{Replace x with y and then solve for y,}\\\\~~~~~~~x = \dfrac 19 y+2\\\\\implies 9x =y + 18~~~~~~~~~~~~~~~;[\text{Multiply both sides by 9}]\\ \\\implies y = 9x -18\\\\\implies f^{-1}(x) = 9x -18\\\\\text{Hence, the inverse of the given function is}~ f^{-1}(x) = 9x -18.$

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Ierofanga [76]

<h3>Solution:</h3>

$1. \frac{w}{2} - 6 = - 10 \\ = > \frac{w}{2} = - 10 + 6 \\ = > \frac{w}{2} = - 4 \\ = > w = - 4 \times 2 \\ = > w = - 8$

$2. \: \: 3x + 3x - 2x = 12 \\ = > 4x = 12 \\ = > x = \frac{12}{4} \\ = > x = 3$

<h3>Answers:</h3>

1. w = -8

2. x = 3

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3 years ago

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3 years ago

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zysi [14]

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3 years ago

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3 years ago