is given by
f(x) = x2 + 4 show that f is invertible with the inverse f-1
of given by 
where R+
is set of all non negative real numbers.
Answer:
Given
f(x) = x2 + 4, Df = R+ = [0, 
)
Injectivity
: Let x1, x2 be any two elements of R+
such that f(x1) = f(x2)
But
both x1 and x2 are positive real numbers
Therefore
x1 = x2
So
f : R+ 
is
one-one.
Surjectivity
: Let 
then y = f(x)
Corresponding
to every element y of 
there
exists a unique element 
such
that 
is onto.
Hence
f is both one-one and onto
To
find inverse of f : 
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