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(Solved): Show that the given functions are inverse functions of each other. Then display the graphs of each ...
Show that the given functions are inverse functions of each other. Then display the graphs of each function and the line \( y \) s s on a graprim caicaiser wa negn thut exch is the image of the other across \( y=x \). \[ y=10^{2 / 2} \text { and } y=2 \log _{10} x \] Transform the function \( y=10^{x / 2} \) to show that if is the inverse of \( y=210 \mathrm{~g} 10^{x} \). \[ \begin{aligned} y=10^{x / 2} \rightarrow \\ \frac{x}{2}-y^{10} \\ \frac{x}{2}=10^{y} \end{aligned} \] \[ y=10^{\frac{y}{2}} \]
\( \frac{y}{2}=\log _{10} x \) \( \frac{x}{2}=10^{x} \) \( \frac{x}{2}=\log _{10} y \) \( \frac{x}{2}=\log _{y} 10 \) \( y=\log _{10} \frac{x}{2} \)
\( y=10^{x / 2} \rightarrow \frac{y}{2}=\log _{10} x \)