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vodomira [7]
2 years ago
15

Give the answer please

Mathematics
1 answer:
Nataliya [291]2 years ago
5 0

The inverse of a function is given as √x - 1

<h3>Inverse of a function</h3>

To get the inverse of any function f(x) we need to ensure that it passes the horizontal line test.

Given the following function

f(x) = (x+1)^2

Let y= f(x) to have:

y = (x+1)^2

Replace y with x to have:

x = (y+1)^2

Make y the subject of the formula

√x =y + 1

Subtract 1 from both sides

√x - 1 = y

Swap

y = √x - 1

Hence the inverse of a function is given as √x - 1

Learn more on inverse of a function here: brainly.com/question/3831584

#SPJ1

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Answer:

Any value of x

<em></em>

Step-by-step explanation:

Given

f(x) = \sqrt{x^2 - 1}

g(x) = \sqrt{x^2 + 1}

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g(f(x)) = \sqrt{(\sqrt{x^2 - 1})^2 + 1}

g(f(x)) = \sqrt{x^2 - 1 + 1}

g(f(x)) = \sqrt{x^2 }

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Equate f(g(x)) and g(f(x))

f(g(x)) = g(f(x))

x = x

<em>This implies that </em>f(g(x)) = g(f(x))<em> at any value of x</em>

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