Answered

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What is the inverse of the function f(x) = 169x2 when x ≥ 0?

A- f−1(x) = 13‾‾
B- f−1(x) = √13
C- f−1(x) = 13x
D- f−1(x) = 113

Sagot :

Answer:

[tex]f^{-1}(x) = \frac{\sqrt{x}}{13}[/tex]

Step-by-step explanation:

Inverse function:

Suppose we have a function y = f(x). To find the inverse, we exchange the y and the x values, and then isolate y.

Function:

[tex]f(x) = 169x^2[/tex]

That is:

[tex]y = 169x^2[/tex]

Exchanging x and y:

[tex]x = 169y^2[/tex]

Isolating y:

[tex]y^2 = \frac{x}{169}[/tex]

[tex]y = \sqrt{\frac{x}{169}}[/tex]

[tex]y = \frac{\sqrt{x}}{13}[/tex]

[tex]f^{-1}(x) = \frac{\sqrt{x}}{13}[/tex]

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