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Question

If the function f(x)=ax+b has its own inverse then the ordered pair (a,b) can be

A
(1,0)
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B
(-1,0)
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C
(-1,1)
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D
(1,1)
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Solution

The correct options are
A (1,0)
B (-1,0)
C (-1,1)
f(x)=a(x)+b
We know that f(f1(x))=x and it is given that f(x) is its own inverse.
Hence
f(f1(x))=a(ax+b)+b
=a2x+b(a+1)
=x
By comparing coefficients, we get
a2=1
a=±1
And b(1+a)=0
b=0 or a=1
Hence the ordered pairs of (a,b) are
(1,1), (1,0), (1,0)

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