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PLEASE HELPPPPPPPP!!

PLEASE HELPPPPPPPP!!-example-1
User Chintan Adatiya
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1 Answer

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Answer:

  • f⁻¹( f⁻¹(13)) = 9
  • f⁻¹(8) = -13

Explanation:

The inverse of a function f(x) denoted by f⁻¹(x) is a function that undoes the f(x) action

To understand this better, let us assume that there is a function f(x) such that f(5) = 25. Then f⁻¹(25) = 5 which was the input for the function f(x)

To generalize,

f⁻¹(f(x)) = x

Dealing with the two questions
f⁻¹( f⁻¹(13))

The evaluation happens from the innermost evaluation to the outermost evaluation

So first determine f⁻¹(13)

Since 13 is an output f⁻¹(13) will give the x value which produced 13. The corresponding x value = 5 from the tables

Now use this in the original expression

f⁻¹( f⁻¹(13)) = f⁻¹(5)

Look at the table and determine where 5 appears in the output. Look at the x value corresponding to that and that will be f⁻¹(5)

From the table we can see that 5 is an output when x = 9 so

f⁻¹(5) = f⁻¹( f⁻¹(13)) = 9

f⁻¹(8)
Relatively easier since this is a straightforward task of locating the value 8 in the f(x) row and seeing what the corresponding x value is

From the table we see that for an output of 8, the input x = -13

So f⁻¹(8) = -13

User Gavin Terrill
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