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NCERT Class XI Mathematics - Relations and Functions - Solutions

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Question : 23
Total: 36
The function ‘t’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by t (C) =
9C
5
+32
Find
(i) t (0)
(ii) t (28)
(iii) t (–10)
(iv) The value of C, when t (C) = 212.
Solution:  
We are given t (C) =
9C
5
+32
(i) t (0) =
9(0)
5
 + 32 = 0 + 32 = 32
(ii) t (28) =
9(28)
5
 + 32 =
252
5
 + 32 =
252+160
5
 =
412
5
 = 82.4
(iii) t (- 10) =
9(−10)
5
 + 32 = - 18 + 32 = 14
(iv) t(C) = 212
⇒
9C
5
 + 32 = 212 ⇒
9C
5
 = 212 - 32 ⇒
9C
5
 = 180 ⇒ C =
180×5
9
 = 100
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