Chapter 5.5, Problem 86AYU

a.

To determine

To calculate; domain of the given relations.

Answer to Problem 86AYU

Solution: $x;$ Domain: $(\infty ,\infty )$

Explanation of Solution

  $f(g(x))={\log }_2(2^x)=x$

  $x;$ Domain: $(\infty ,\infty )$

b.

To determine

To calculate; domain of the given relations.

Answer to Problem 86AYU

Solution: $x;$ Domain: $(\infty ,\infty )$

Explanation of Solution

  $g(f(x))=2^{{\log }_{2}x}=x$

  $x;$ Domain: $(\infty ,\infty )$

c.

To determine

To calculate; domain of the given relations.

Answer to Problem 86AYU

Solution: $(f\circ g)(3)=3$

Explanation of Solution

  $(f\circ g)(x)={\log }_2{2}^x=x$

  $(f\circ g)(3)=3$

d.

To determine

To calculate; domain of the given relations.

Answer to Problem 86AYU

Solution: $(0,\infty )$

Explanation of Solution

  $(f\circ h)(x)={\log }_{2}4x$

The domain is: $(0,\infty )$

e.

To determine

To calculate; domain of the given relations.

Answer to Problem 86AYU

Solution: $(f\circ h)(8)=5$

Explanation of Solution

  $\begin{array}{l}(f\circ h)(x)={\log }_{2}4x\\ (f\circ h)(e)={\log }_{2}4(8)\\ (f\circ h)(8)=5\end{array}$