Check whether the given functions are inverse of each others:1) g ( x ) =...

termegolz6

termegolz6

Answered

2022-07-25

Check whether the given functions are inverse of each others:
1) g ( x ) = x 2 3 f ( x ) = x 3 5
2) g ( x ) = 4 x x f ( x ) = 4 x
3) f ( x ) = x 1 x 2 g ( x ) = 2 x + 1 x 1
4) h ( x ) = 2 2 x x f ( x ) = 2 x + 2

Answer & Explanation

iljovskint

iljovskint

Expert

2022-07-26Added 18 answers

Step 1
1) g ( x ) = x 5 3 l e t   g ( x ) = y x 5 3 = y x 5 y + 3 x 5 = y 3 x = ( y 3 ) 1 / 5
g ( x ) = f ( x ) = x 3 5 7 8
2) g ( x ) 4 x x f ( x ) = 4 x l e t   g ( x ) = y 4 x x = y 4 x = y 4 2 = y + 1 x = 4 y + 1
Step 2
3) f ( x ) = x 1 x 2 l e t   y = x 1 x 2 y x 2 y = x 1 y x + x = 1 + 2 y x ( y + 1 ) = 1 + 2 y x = 1 + 2 y y + 1 f ( x ) g ( x )
4) h ( x ) = 2 2 x x l e t   y = 2 2 x x y = 2 x 2 y + 2 = 2 x x = 2 y + 2 = 7 ( x )

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