Find g o f and f o g , if (i) (ii)

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Solution

(i)

The functions provided are f( x )=| x | and g( x )=| 5x−2 |

( gof )( x )=g( f( x ) ) =g( | x | ) =| 5| x |−2 |

( fog )( x )=f( g( x ) ) =f( | 5x−2 | ) =| | 5x−2 | | =| 5x−2 |

Thus, the function ( fog )( x ) is | 5x−2 | and ( gof )( x ) is | 5| x |−2 |

(ii)

The functions provided are f( x )=8 x 3 and g( x )= x 1 3 .

( gof )( x )=g( f( x ) ) =g( 8 x 3 ) = ( 8 x 3 ) 1 3 =2x

( fog )( x )=f( g( x ) ) =f( x 1 3 ) =8 ( x 3 ) 1 3 =8x

Thus, the function ( fog )( x ) is 8x and ( gof )( x ) is 2x .

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