Maths-
General
Easy

Question

The inverse of the function y equals open square brackets 1 minus left parenthesis x minus 3 right parenthesis to the power of 4 end exponent close square brackets to the power of 1 divided by 7 end exponent is

  1. 3 plus open parentheses 1 minus x to the power of 7 end exponent close parentheses to the power of fraction numerator 1 over denominator 4 end fraction end exponent    
  2. open parentheses 3 minus open parentheses 1 minus x to the power of 7 close parentheses to the power of 1 fourth end exponent close    
  3. 3 minus open parentheses 1 plus x to the power of 7 end exponent close parentheses to the power of fraction numerator 1 over denominator 4 end fraction end exponent    
  4. 3 plus open parentheses 1 plus x to the power of 7 end exponent close parentheses to the power of fraction numerator 1 over denominator 4 end fraction end exponent    

hintHint:

We are given a function. We have to find it's inverse. To find an inverse, we will interchange the variables. We will replace x by y and y by x. Then we will find the equation in terms of y.

The correct answer is: 3 plus open parentheses 1 minus x to the power of 7 end exponent close parentheses to the power of fraction numerator 1 over denominator 4 end fraction end exponent


    The given function is y = left parenthesis 1 minus open parentheses x minus 3 close parentheses to the power of 4 right square bracket to the power of 1 divided by 7 end exponent 
    The first step will be to interchange the variables.
    We get
    x equals left square bracket 1 minus open parentheses y minus 3 close parentheses to the power of 4 right square bracket to the power of 1 over 7 end exponent
    Now, we will find the above equation in terms of y.
    x equals left square bracket 1 minus open parentheses y minus 3 close parentheses to the power of 4 right square bracket to the power of 1 over 7 end exponent W e space w i l l space r a i s e space b o t h space t h e space s i d e s space t o space t h e space p o w e r space o f space 7
x to the power of 7 equals open square brackets 1 minus left parenthesis y minus 3 right parenthesis to the power of 4 close square brackets to the power of 1 over 7 cross times 7 end exponent
x to the power of 7 equals 1 minus left parenthesis y minus 3 right parenthesis to the power of 4 R e a r r a n g i n g space t h e space e q u a t i o n
left parenthesis y minus 3 right parenthesis to the power of 4 equals 1 minus x to the power of 7
W e space w i l l space t a k e space f o u r t h space r o o t space o f space b o t h space t h e space s i d e s
left parenthesis y minus 3 right parenthesis to the power of 4 cross times 1 fourth end exponent equals left parenthesis 1 minus x to the power of 7 right parenthesis to the power of 1 fourth end exponent y minus 3 space equals left parenthesis 1 minus x to the power of 7 right parenthesis to the power of 1 fourth end exponent W e space w i l l space a d d space 3 space t o space b o t h space t h e space s i d e s.
y space equals space 3 space plus space left parenthesis 1 space minus x to the power of 7 right parenthesis to the power of 1 fourth end exponent
    This is the required answer.

    We used rules of indices to solve the question. For such questions, we should be familiar with rules of indices.

    Related Questions to study

    General
    Maths-

    The domain of f left parenthesis x right parenthesis equals square root of x to the power of 2 end exponent minus 4 vertical line x vertical line plus 3 end root is

    The domain of f left parenthesis x right parenthesis equals square root of x to the power of 2 end exponent minus 4 vertical line x vertical line plus 3 end root is

    Maths-General
    General
    physics

    A Shell of mass M and radius R has a point mass  placed at a distance r from its center. The gravitational potential energy u(r)-v will be,

    A Shell of mass M and radius R has a point mass  placed at a distance r from its center. The gravitational potential energy u(r)-v will be,

    physicsGeneral
    General
    Physics

    The correct graph representing the variation of total energy (E) kinetic energy  and potential energy (U) of a satellite with its distance from the center of earth is.........

    The correct graph representing the variation of total energy (E) kinetic energy  and potential energy (U) of a satellite with its distance from the center of earth is.........

    PhysicsGeneral
    parallel
    General
    physics

    The curves for P.E. (U) K.E. (EEK) of two particle system ae shown in figure, At what points. system will be bound.

    The curves for P.E. (U) K.E. (EEK) of two particle system ae shown in figure, At what points. system will be bound.

    physicsGeneral
    General
    chemistry-

    The absolute configuration of the following compound is :

    The absolute configuration of the following compound is :

    chemistry-General
    General
    chemistry-

    The name of the compound is 

    The name of the compound is 

    chemistry-General
    parallel
    General
    chemistry-

    Among the following structures which one is called Erythro isomer ?

    Among the following structures which one is called Erythro isomer ?

    chemistry-General
    General
    chemistry-

    How many stereo isomers are there in this compound ?

    How many stereo isomers are there in this compound ?

    chemistry-General
    General
    chemistry-

    The compound is known by which of the following names ?

    The compound is known by which of the following names ?

    chemistry-General
    parallel
    General
    chemistry-

    Which of the following structures have same configuration around the chirality centre ?

    Which of the following structures have same configuration around the chirality centre ?

    chemistry-General
    General
    chemistry-

    The two structures given below are :

    The two structures given below are :

    chemistry-General
    General
    chemistry-

    Which of the following represents same enantiomer as :

    Which of the following represents same enantiomer as :

    chemistry-General
    parallel
    General
    chemistry-

    Calculate the d- and l-isomers formed by the following compound.
    H O O C minus C H open parentheses C H subscript 3 end subscript close parentheses minus C H O H minus C H B r minus C H O H minus C H open parentheses C H subscript 3 end subscript close parentheses minus C O O H minus

    Calculate the d- and l-isomers formed by the following compound.
    H O O C minus C H open parentheses C H subscript 3 end subscript close parentheses minus C H O H minus C H B r minus C H O H minus C H open parentheses C H subscript 3 end subscript close parentheses minus C O O H minus

    chemistry-General
    General
    physics

    Which of the following graphs represents the motion of a planet moving about the sun.

    Which of the following graphs represents the motion of a planet moving about the sun.

    physicsGeneral
    General
    chemistry-

    The configuration of 1 and 2 carbon atom in the following compounds is –

    The configuration of 1 and 2 carbon atom in the following compounds is –

    chemistry-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.