Let begin mathsize 12px style f colon N rightwards arrow Y space b e space a space f u n c t i o n space d e f i n e d space a s space f left parenthesis x right parenthesis equals 4 x plus 3 space w h e r e space Y equals open curly brackets y element of N colon y equals 4 x plus 3 space f o r space s o m e space x element of N close curly brackets. S h o w space t h a t space f space i s space i n v e r t i b l e space a n d space i t s space i n v e r s e space i s
i. g open parentheses y close parentheses equals fraction numerator 3 y plus 4 over denominator 3 end fraction space space space i i. g open parentheses y close parentheses equals 4 plus fraction numerator y plus 3 over denominator 4 end fraction space space space i i i. g open parentheses y close parentheses equals fraction numerator y plus 3 over denominator 4 end fraction space space space i v. g open parentheses y close parentheses equals fraction numerator y minus 3 over denominator 4 end fraction end style

Asked by sunil2791 | 3rd Jun, 2017, 05:50: PM

Expert Answer:

begin mathsize 16px style straight f open parentheses straight x close parentheses equals 4 straight x plus 3
Show space that space function space is space one space one space and space onto space then space find space its space inverse.
Let comma space straight f left parenthesis straight x subscript 1 right parenthesis equals straight f left parenthesis straight x subscript 2 right parenthesis
rightwards double arrow 4 straight x subscript 1 plus 3 equals 4 straight x subscript 2 plus 3
rightwards double arrow straight x subscript 1 equals straight x subscript 2
straight f space is space one minus one.
Let space straight f left parenthesis straight x right parenthesis equals straight y
straight y equals 4 straight x plus 3
straight y minus 3 equals 4 straight x
straight x equals fraction numerator straight y minus 3 over denominator 4 end fraction
If space you space put space this space value space in space straight f left parenthesis straight x right parenthesis space you space will space get space equals space straight y.
So space it space is space onto space function space also end style

Answered by Sneha shidid | 5th Jun, 2017, 11:30: AM