## About "Find Values of Inverse Functions from Tables"

Find Values of Inverse Functions from Tables

Here we are going to see how to find values of inverse functions from the graph.

A function is a rule that says each input (x-value) to exactly one output (f(x)- or y-value).

A function is invertible if each possible output is produced by exactly one input. If a function f(x) is invertible, its inverse is written f-1(x).

The inverse f-1(x) takes output values of f(x) and produces input values.

That is  :  f-1(b)  =  a if and only if f(a)  =  b

Question 1 :

Use the table below to find the following if possible :

(i)  f -1(- 4)

(ii)  f -1(6)

(iii)  f -1(9)

(iv)  f -1(10)

(v)  f -1(-10) Solution :

(i)  f -1(- 4)

a = f -1(- 4)  if and only if - 4 = f(a)

By considering the table, we have to check for which value of x, we have the value -4 for f(x).

For f(6), we have -4.

Hence f-1 (4)  =  6

(ii) f -1(6)

b = f -1(6)  if and only if 6 = f(b)

We don't find the value 6 in the column f(x). Hence f -1(6) is undefined.

(iii)  f -1(9)

c = f -1(9)  if and only if 9 = f(c)

In the column f(x), we have 9 in the first row.The corresponding value f(4) is 9

Hence f-1 (9)  =  4

(iv)  f -1(10)

d = f -1(10)  if and only if 10 = f(d)

We don't find the value 6 in the column f(x). Hence f -1(10) is undefined.

(v)  f -1(-10)

In the column f(x), we have -10 in the last row.The corresponding value f(8) is -10.

Hence f-1 (10)  =  8. After having gone through the stuff given above, we hope that the students would have understood "Find Values of Inverse Functions from Tables".

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