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Question

Show that the function f in A =R=23 defined by f(x)=3x+25x+3, 35 is one-one and onto.Hence find f1(x)

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Solution

f(x)=3x+25x+3,x35

One One:

3x1+25x1+3=3x2+25x2+3

15x1x2+9x1+10x2+6=15x1x2+9x2+10x1+6

x2=x1

f is one-one

Onto:

Let y=3x+25x+3

5xy+3y=3x+2

(5y3)x=23y

x=23y5y3

Now, f(23y5y3)=3(23y5y3)+25(23y5y3)+3

=69y+10y61015y+15y9

=y

f is onto

and f1(x)=23x5x3


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