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The table below shows some inputs and outputs of the invertible function f with domain all real numbers.

x | 14 | -6 | -1 | 10 | -10 | 3
f(x) | 7 | -10 | -15 | 14 | -4 | -9

Find the following values:

f^-1(f^-1(7)) = ?
f^-1(-4) = ?

The table below shows some inputs and outputs of the invertible function f with domain all real numbers x 14 6 1 10 10 3 fx 7 10 15 14 4 9 Find the following va class=

Respuesta :

Answer for the first box = 10

Answer for the second box =  -10

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Work Shown:

f(x) is a function where we plug in the given row of x values to have them lead to the corresponding f(x) values in the table. We see that x = 14 leads to y = f(x) = 7. Going backwards, we can say [tex]f^{-1}(7) = 14[/tex]. The inverse simply undoes everything f(x) does.

So,

[tex]f^{-1}(f^{-1}(7)) = f^{-1}(14) = 10[/tex]

For the portion [tex]f^{-1}(14) = 10[/tex], look at the column that has x = 10. This shows it leading to f(x) = 14. You trace this column upward to go backward to undo f(x).

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That takes care of the first part. The second part is pretty much the same idea. We locate where -4 is in the bottom row, and then we write down the corresponding x value.

We see that y = -4 pairs with x = -10, which is why [tex]f^{-1}(-4) = -10[/tex]

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Keep in mind that this function must be one-to-one for the inverse to exist. If not, then you'll have to do some kind of domain restriction.

The answer of the first table is 10 and the answer of the second table is -10.

What is a function?

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.

Given that data set

x | 14 | -6 | -1 | 10 | -10 | 3

f(x) | 7 | -10 | -15 | 14 | -4 | -9

now at x =14 , f(x) = 7

f(14) = 7 ⇒ [tex](f^-(7))[/tex] = 14

Now at x =-10 , f(x) = 14

f(10) = 14 now since f inverse of f inverse 7  is equal to f inverse 14 so from here

[tex](f^-(14))[/tex] = [tex]f^-(f^-(7))[/tex] = 10 hence it will be the correct answer for the first block.

Now for the second block at x = -10 , f(x) = -4 so

[tex](f^-(-4))[/tex] = -10 hence it will be the correct answer for the second block.

For more about the function

brainly.com/question/23712366

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