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Show that f : [–1, 1] → R, given by is one-one. Find the in...

Show that f : [–1, 1] → R, gi | Class 12 Mathematics Chapter Relations and Functions, Relations and Functions NCERT Solutions

Question:

Show that f : [–1, 1] → R, given by is one-one. Find the inverse of the function f : [–1, 1] → Range f.

(Hint: For y ∈ Range f, y =, for some x in [ - 1, 1], i.e.,)

Answer:

f: [ - 1, 1] → R is given as

Let f(x) = f(y).

∴ f is a one-one function.

It is clear that f: [ - 1, 1] → Range f is onto.

∴ f: [ - 1, 1]→ Range f is one-one and onto and therefore, the inverse of the function:

f: [ - 1, 1] → Range f exists.

Let g: Range f → [ - 1, 1] be the inverse of f.

Let y be an arbitrary element of range f.

Since f: [ - 1, 1] → Range f is onto, we have:

Now, let us define g: Range f → [ - 1, 1] as

∴gof =I_{[-1, 1]}and fog = I_{Range f}

∴ f - 1 = g

⇒

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Comments

VIDIT
2019-05-03 14:20:46

WHERE IS THE RANGE OF THE FUNCTION

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Welcome to the NCERT Solutions for Class 12 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 3 , Question 6: Show that f : [–1, 1] → R, given by is one-one. Find the inverse of the function f :....

Show that f : [–1, 1] → R, gi | Class 12 Mathematics Chapter Relations and Functions, Relations and Functions NCERT Solutions

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