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Olin [163]
2 years ago
14

For the function f(x)

Mathematics
1 answer:
WITCHER [35]2 years ago
4 0

Given:

The function is

f(x)=\dfrac{8\sqrt[3]{x}-8}{9}

To find:

The inverse function f^{-1}(x).

Solution:

We have,

f(x)=\dfrac{8\sqrt[3]{x}-8}{9}

Step 1: Putting f(x)=y, we get

y=\dfrac{8\sqrt[3]{x}-8}{9}

Step 2: Interchange x and y.

x=\dfrac{8\sqrt[3]{y}-8}{9}

Step 3: Isolate variable y.

9x=8\sqrt[3]{y}-8

9x+8=8\sqrt[3]{y}

\dfrac{9x+8}{8}=\sqrt[3]{y}

Taking cube on both sides, we get

\left(\dfrac{9x+8}{8}\right)^3=y

y=\left(\dfrac{9x+8}{8}\right)^3

Step 4: Putting y=f^{-1}(x), we get

f^{-1}(x)=\left(\dfrac{9x+8}{8}\right)^3

Therefore, the correct option is C.

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