Question

Check whether the function f: : R → R defined as f (x) = x

3

is one-one or not.​

Answer 1

Answer:

Let x and y be two elements of domain (R),

such that

⇒ f (x)=f (y)

⇒ x³ + 4 = y³+4

⇒x³ = y³

⇒x = y

:: f is one -one .

onto test for f :

Let be in the co- domain (R), such that,

⇒f (x) = y

⇒x² + 4 = y

⇒ x = ³√ y- 4 € R (Domain)

∴ f is onto.

Since, f is one-one and onto then it is bijective.

∴ f is invertible

Let f -¹ (x) = y

⇒x = y³ + 4

⇒x = 4 = y³

⇒y = ³√x-4

From ( 1 ),

⇒f -¹ (x) = ³√ x - 4

⇒f -¹ (3) = ³√3 - 4

=³√- 1

= - 1

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