Question

Question 8 Let f = {(1, 1), (2, 3), (0, –1), (–1, –3)} be a function from Z to Z defined by f(x) = ax + b, for some integers a, b. Determine a, b.

Class X1 - Maths -Relations and Functions Page 46

Answer 1

(0,-1) belongs to the function
a.0+b=-1
b=-1
(1,1) belongs to the function
a.1+b=1
Substitute b value =-1
a-1=1
a=1+1=2.
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Answer 2

Here,
f(x) = {(1,1),(2,3),(0,-1),(-1,-3)}, it means value of f(x) = 1,3,-1,-3 when value of x is 1,2,0,-1 respectively.

But f(x) is defined by
f(x) = ax + b
so, put x = 1 and f(x) = 1
Then, 1 = a.1 + b
a + b = 1 ____________(1)
again, put
x = 2, and f(x) = 3
3 = a.2 + b
3 = 2a + b ___________(2)

solve both equations
And we get a = 2, b = -1
Hence, f(x) = 2x - 1