Answered

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FUNCTIONS

h(x)= 3^x

a) Solve the equation h^-1(x)= 2

Sagot :

Crisforpidn
Because the inverse of function h(x) = 3^x is h^-1 ( x ) = log 3 ( x ) , we solve the equation log 3 ( x ) = 2 ;
3^2 = x;
x = 9 ;
Naǫidn
Use the property of inverse functions:
[tex]h(h^{-1}(x))=x \\ \\ \hbox{if} \\ h^{-1}(x)=2 \\ \hbox{then} \\ h(2)=x \\ \Downarrow \\ h(x)=3^x \\ h(2)=3^2 \\ h(2)=9 \\ \\ \boxed{x=9} [/tex]
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