Let's solve the problem step-by-step to find [tex]\( f(g(5)) \)[/tex].
1. Define the inner function [tex]\( g(x) \)[/tex]:
[tex]\[
g(x) = x^2 - 5x
\][/tex]
2. Substitute [tex]\( x = 5 \)[/tex] into [tex]\( g(x) \)[/tex]:
[tex]\[
g(5) = 5^2 - 5 \cdot 5
\][/tex]
3. Calculate the value of [tex]\( g(5) \)[/tex]:
[tex]\[
g(5) = 25 - 25 = 0
\][/tex]
4. Now, substitute [tex]\( g(5) \)[/tex] into the outer function [tex]\( f(u) \)[/tex], where [tex]\( u = g(5) \)[/tex]:
[tex]\[
f(u) = \sqrt{u}
\][/tex]
Since [tex]\( u = g(5) = 0 \)[/tex], we substitute [tex]\( 0 \)[/tex] into [tex]\( f(u) \)[/tex]:
[tex]\[
f(g(5)) = f(0) = \sqrt{0}
\][/tex]
5. Calculate the value of [tex]\( \sqrt{0} \)[/tex]:
[tex]\[
\sqrt{0} = 0
\][/tex]
Therefore, the value of [tex]\( f(g(5)) \)[/tex] is:
[tex]\[
f(g(5)) = 0
\][/tex]
