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For the function f(x)
8 Vas - 8. find / -'(X).
9
+8
of-'() = (9)
O/(x) = 9(+8)
O!'(x) = (18)
Of(x) = 9(2+8)
8
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For The Function Fx 8 Vas 8 Find X 9 8 Of 9 Ox 98 Ox 18 Ofx 928 8 Submit Answer class=

Sagot :

Given:

The function is

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

To find:

The inverse function [tex]f^{-1}(x)[/tex].

Solution:

We have,

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

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

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

Step 2: Interchange x and y.

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

Step 3: Isolate variable y.

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

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

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

Taking cube on both sides, we get

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

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

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

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

Therefore, the correct option is C.

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