Failed to connect to MySQL: Access denied for user 'examnext_online'@'localhost' (using password: YES) The function ƒ `[a, oo) -> R` where R denotes the range corresponding to the given domain, with rule ƒ(x) =` 2x^3 – 3x^2 + 6,` will have an inverse provided - Sarthaks eConnect

The function ƒ : `[a, oo) -> R` where R denotes the range corresponding to the given domain, with rule ƒ(x) =` 2x^3 – 3x^2 + 6,` will have an inverse provided

The function ƒ : `[a, oo) -> R` where R denotes the range corresponding to the given domain, with rule ƒ(x) =` 2x^3 – 3x^2 + 6,` will have an inverse provided

A.

`a<=1`

B.

`a>=0`

C.

`a<=0`

D.

`a>=1`

Solution

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Best answer

`ƒ(x) = 2x^3 –3x^2 + 6`

`ƒ'(x) = 6x^2 – 6x = 6(x^2 – x)`

`ƒ'(x) = 0 => 6(x^2 – x) = 0 `

`=>x = 0 or x = 1`

For inverse to exist, functon must be one-one onto. Hence, the domain is [1, `oo`) Hence, a `>=`1.