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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