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The inverse of the function   y=\left [ 1-\left ( x-3 \right )^{4} \right ]^{\frac{1}{7}}  is

  • Option 1)

    3+\left ( 1-x^{7} \right )^{\frac{1}{4}}

  • Option 2)

    3-\left ( 1+x^{7} \right )^{\frac{1}{4}}

  • Option 3)

    3-\left ( 1-x^{7} \right )^{\frac{1}{4}}

  • Option 4)

    None of these

 

Answers (1)

As we learnt in 

Co - Domain of function -

All possible outcomes for the function f(x) is known as co - domain unless not specified in question.

-

 

 

Range of function -

All possible values of  f(x)\: \: \forall x\in domain  (f) is known as Range 

-

 

 y=\left [1 -(x-3)^{4} \right ]^\frac{1}{7}

y^{7}=1-(x-3)^{4}

\therefore (x-3)^{4}=1-y^{7}

x=3+(1-y^{7})^\frac{1}{4}

f^{-1}(x)=3+(1-x^{7})^\frac{1}{4}


Option 1)

3+\left ( 1-x^{7} \right )^{\frac{1}{4}}

Option is correct

Option 2)

3-\left ( 1+x^{7} \right )^{\frac{1}{4}}

Option is incorrect

Option 3)

3-\left ( 1-x^{7} \right )^{\frac{1}{4}}

Option is incorrect

Option 4)

None of these

Option is incorrect

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