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Question 7

 Consider f : R → R given by f(x) = 4x + 3. Show that f is invertible. Find the inverse of f

Answer

fR → R is given by,

f(x) = 4x + 3

One-one:

Let f(x) = f(y).

∴ f is a one-one function.

Onto:

For y ∈ R, let y = 4x + 3.

Therefore, for any y ∈ R,   such that

∴ f is onto.

Thus, f is one-one and onto and therefore, f - 1 exists.

Let us define gR→ R by.

Hence, f is invertible and the inverse of f is given by

 

 

Popular Questions of Class 12th mathematics

 

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Let A = R – {3} and B = R – {1}. Consider the function  f : A → B defined by

. Is f one-one and onto? Justify your answer. 

 

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