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INVERSE FUNCTION
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tions are inverses by finding their composite 
u(a(u)), which equals 0.53(1.90u)
and simplifies to equal 
u.
Inverses are also used to decode secret messages. If an encrypting pattern is
used to change the letters in a sentence, then a decrypting pattern is needed to
place the letters back in their normal positions. For example, suppose an encryp-
tion function of 
e(w) = 2w + 3 is applied to each letter in a word, where letters
had corresponding numbers (e.g., a = 1, b = 2, c = 3, . . . z = 26). The word
“math” would first translate to a numerical expression, 13 1 20 8, and then be
transformed using the function 
e(w) = 2w + 3, where w represents the original
number, and 
e represents the coded number. So the letter “m,” equivalent to 13,
would transform to 
e = 2(13) + 3 = 29. After transforming 1, 20, and 8, the
final coded expression would be 29 5 43 19. If you receive the secret transmis-
sion of an encoded expression 29 5 43 19, you will need to decode it using the
inverse function, 
w(e). One way to find this inverse is to solve for w in the equa-
tion
e = 2w + 3 by subtracting 3 from both sides and then dividing by 2. Thus 
w =
e
−3
2
is the inverse operation that will decode the expression. The first num-
ber, 29, would be converted to 
w =
29−3
2
= 13, which translates to the letter “m” 
in the alphabet. If you apply the inverse function to the remaining numbers 5 43
19, you will obtain the word “math” again. Encrypted codes that deal with con-
fidential information, such as credit card numbers and highly classified material,
are far more complex than this function. However, the decryption of obscure
codes is often performed by computers that use a program that relies on the
process of an inverse operation! (For a more secure code, see Matrices.)
online sources for further exploration
Cryptology



Inverse problems in the earth sciences

Universal currency converter


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