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matrenka [14]
3 years ago
5

Help me please!

Mathematics
1 answer:
telo118 [61]3 years ago
7 0

Answer:

f^{-1}(6) = 50

Step-by-step explanation:

Given

f(x) = \sqrt{2x} - 4

Required

Find f^{-1}(6)

First, we calculate the inverse function

f(x) = \sqrt{2x} - 4

Express f(x) as y

y = \sqrt{2x} - 4

Swap the positions of x and y

x = \sqrt{2y} - 4

Solve for y: Add 4 to both sides

4 + x = \sqrt{2y} - 4+4

4 + x = \sqrt{2y}

Square both sides

(4 + x)^2 = 2y

Divide both sides by 2

y = \frac{(4 + x)^2}{2}

Express y as an inverse function

f^{-1}(x) = \frac{(4 + x)^2}{2}

Next, solve for: f^{-1}(6)

Substitute 6 for x

f^{-1}(6) = \frac{(4 + 6)^2}{2}

f^{-1}(6) = \frac{(10)^2}{2}

f^{-1}(6) = \frac{100}{2}

f^{-1}(6) = 50

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