3 years ago

Please help with 11 and 12

Mathematics

1 answer:

larisa [96]3 years ago

7 0

11.k>-3(4r+3)/4r-5
12.k<(2x+2)/x+3

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If f(x)=69-15x then $f(f^{-1}(x))=x$

Given :

$f(x)=69-15x\\$

Lets find out $f^{-1}(x)$ . The steps to find out f inverse are

Replace f(x) by y

$y=69-15x\\Interchange \; the \; variables\\x=69-15y\\solve \; for \; y\\x-69=-15y\\Divide \; by \; -15\\\frac{-x+69}{15} =y\\Replace \;y \;with \; f^{-1}\\f^{-1}=\frac{-x+69}{15}$

Now we find $f(f^{-1}(x))$

Replace inverse function in the place of x in f(x)

$f(f^{-1}(x))=f(\frac{-x+69}{15} )=69-15(\frac{-x+69}{15})=69-(-x+69)=69+x-69=x\\f(f^{-1}(x))=x$

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