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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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Read 2 more answers
GEOMETRY Kymani has two equal-sized large pitchers and two equal-sized small pitchers. All of the pitchers together hold 40 cups
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Each of the small pitcher will contain 4 cups of water while each of the large pitcher will contain 16 cups of water.

Therefore,  two equal-sized large pitchers will hold 32 cups of water while the two equal-sized small pitchers will hold 8 cups of water

<h3>Larger Pitchers</h3>

The 2 larger pitchers are equal in size.

Let

each size of the large pitcher = x

Two large size pitcher = 2x

<h3>Smaller Pitchers</h3>

The 2 smaller pitchers are equal in size

let

each size of the pitcher = y

Two small sized pitchers = 2y

<h3>Pitchers Capacities</h3>

The whole pitchers holds 40 cups of water. Therefore,

  • 2x + 2y = 40

The capacity of one large pitcher minus the capacity of one small pitcher is 12 cups. Therefore,

  • x - y  = 12

Combine the equations.

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x - y = 12

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y = 8 / 2

y = 4

x - 4 = 12

x = 12 + 4

x = 16

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