FIND VALUES OF INVERSE FUNCTION FROM TABLES

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

Example :

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 f(a) = -4

In the above table, f(x) = -4 for x = 6.

f(6) = -4

f-1(-4) = 6

(ii) f-1(6)

a = f-1(6) if and only if 6 = f(a)

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 f(c) = 9

In the above table, f(x) = 9 for x = -4.

f(-4) = 9

f-1(9) = -4

(ivf-1(10)

d = f-1(10) if and only if f(d) = 10.

We don't find the value 10 in the column f(x).

Hence f-1(10) is undefined.-

(v) f-1(-10)

e = f-1(-10) if and only if f(e) = -10.

In the above table, f(x) = -10 for x = 8.

f(8) = -10

f-1(-10) = 8

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