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kaheart [24]
3 years ago
8

Helppp!! I NEED HELP PLEASE

Mathematics
1 answer:
Elodia [21]3 years ago
5 0

Given:

The table of values for the function f(x).

To find:

The values f^{-1}(f(3.14)) and f(f(-7)).

Solution:

From the given table, it is clear that the function f(x) is defined as:

f(x)=\{(-14,11),(-7,-12),(-12,-5),(9,1),(10,-2),(-2,13)\}

We know that if (a,b) is in the function f(x), then (b,a) must be in the function f^{-1}(x). So, the inverse function is defined as:

f^{-1}(x)=\{(11,-14),(-12,-7),(-5,-12),(1,9),(-2,10),(13,-2)\}

And,

f^{-1}(f(a))=f^{1}(b)

f^{-1}(f(a))=a              ...(i)

Using (i), we get

f^{-1}(f(3.14))=3.14

Now,

f(f(-7))=f(-12)

f(f(-7))=5

Therefore, the required values are f^{-1}(f(3.14))=3.14 and f(f(-7))=5.

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