Q. 44

If a function g = {(1, 1), (2, 3), (3, 5), (4, 7)} is described by g(x) = αx + β, find the values of α and β.

Class 12th RD Sharma - Volume 1 2. Functions

Answer :

Given:-

(i)g={(1, 1), (2, 3), (3, 5), (4, 7)}

(ii)g(x) = αx + β

For x=1 and αx + β

g(1)=α(1)+ β=1

⇒ α+ β=1

For x=2

g(2)=α(2)- β=3

⇒ 2α- β=3

Similarly with g(3) and g(4)

Using above value

α=2

β=1

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PREVIOUSIf the mapping f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3}, given byf = {(1, 2), (3, 5), (4, 1)} and g = {(2, 3), (5, 1), (1, 3), write fog.NEXTIf f(x) = 4 – (x – 7)3, write f–1(x).

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