Sets Practice Test 1

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Question : 8 of 33

Marks: +1, -0

Let f : R → R defined by

f(x) = x^ 2 - 1

, then the value of

f^{ -1} (24)

and

f ^{-1} (-5)

respectively are

ϕ, {3, -3}
{5, -5}, ϕ
{3, -3}, ϕ
ϕ, {5, -5}
None of these

Solution:

Let

y = x^ 2 - 1

, then for y = 24 we have

y = x^2 - 1

24 = x^2 - 1

x^2 = 25

x = ± 5

And for y = -5, x becomes imaginary.
So, there is no value of x.
Hence,

f^{-1}(24)

{5, -5} and

f^{-1}(-5)

= ϕ

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