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Rashid [163]
3 years ago
5

The function f(x) = 9x +5 is one-to-one. Find an equation for f-'(x), the inverse function.

Mathematics
1 answer:
Gnesinka [82]3 years ago
8 0

Answer:

The inverse function is f^{-1}(x) = \frac{x - 5}{9}

Step-by-step explanation:

Inverse function:

Suppose we have a one-to-one function y = f(x). To find it's inverse, we exchange y and x, and then isolate y.

In this question:

y = 9x + 5

Exchanging x and y:

x = 9y + 5

Isolating y:

9y = x - 5

y = \frac{x - 5}{9}

f^{-1}(x) = \frac{x - 5}{9}

The inverse function is f^{-1}(x) = \frac{x - 5}{9}

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