karush
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MHB
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Let $$f(x) = k\ log_2 x$$
(a) Given that $$f^{-1}(1)=8$$, find the value of $$k$$
to get $$f^{-1}(x)$$ exchange $$x$$ and $$y$$
$$x=log_2 y^k$$
then convert to exponential form
$$2^x=y^k $$ then $$2^{\frac{x}{k}} = y$$
so for $$f^{-1}(1) = 2^{\frac{1}{k}}= 8=2^3$$ then $$\frac{1}{k}=3$$ so $$k=\frac{1}{3}$$
(b) find $$f^{-1}\bigg(\frac{2}{3}\bigg)=2^{\frac{2}{3}\frac{3}{1}}=2^2=4$$
(a) Given that $$f^{-1}(1)=8$$, find the value of $$k$$
to get $$f^{-1}(x)$$ exchange $$x$$ and $$y$$
$$x=log_2 y^k$$
then convert to exponential form
$$2^x=y^k $$ then $$2^{\frac{x}{k}} = y$$
so for $$f^{-1}(1) = 2^{\frac{1}{k}}= 8=2^3$$ then $$\frac{1}{k}=3$$ so $$k=\frac{1}{3}$$
(b) find $$f^{-1}\bigg(\frac{2}{3}\bigg)=2^{\frac{2}{3}\frac{3}{1}}=2^2=4$$