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Andre45 [30]
3 years ago
11

Find the f^-1(x) and it’s domain

Mathematics
1 answer:
borishaifa [10]3 years ago
3 0

Answer:

f^{-1}(x) = (x + 8)^2

x \ge -8

Step-by-step explanation:

Given

f(x) = \sqrt x - 8

Solving (a): f^{-1}(x)

We have:

f(x) = \sqrt x - 8

Express f(x) as y

y = \sqrt x - 8

Swap x and y

x = \sqrt y - 8

Add 8 to both\ sides

x + 8 = \sqrt y - 8 + 8

x + 8 = \sqrt y

Square both sides

(x + 8)^2 = y

Rewrite as:

y = (x + 8)^2

Express y as: f^{-1}(x)

f^{-1}(x) = (x + 8)^2

To determine the domain, we have:

The original function is f(x) = \sqrt x - 8

The range of this is: f(x) \ge -8

The domain of the inverse function is the range of the original function.

<em>Hence, the domain is:</em>

x \ge -8

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