Find Values of Inverse Functions from Tables

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

(iv) f^-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

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.