To solve the given problem, we need to find [tex]\( f(g(5)) \)[/tex] where [tex]\( f(x) = x^2 - 4x \)[/tex] and [tex]\( g(x) = 2x - 3 \)[/tex]. Let's break this down step by step.
1. Calculate [tex]\( g(5) \)[/tex]:
We start by finding the value of [tex]\( g(5) \)[/tex]. Plug [tex]\( x = 5 \)[/tex] into the function [tex]\( g(x) \)[/tex]:
[tex]\[
g(5) = 2(5) - 3
\][/tex]
Simplify the expression:
[tex]\[
g(5) = 10 - 3 = 7
\][/tex]
So, [tex]\( g(5) = 7 \)[/tex].
2. Calculate [tex]\( f(g(5)) \)[/tex]:
Now that we have [tex]\( g(5) = 7 \)[/tex], we need to find [tex]\( f(7) \)[/tex] by substituting [tex]\( x = 7 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(7) = 7^2 - 4(7)
\][/tex]
Simplify the expression:
[tex]\[
f(7) = 49 - 28 = 21
\][/tex]
So, [tex]\( f(7) = 21 \)[/tex].
3. Conclusion:
Therefore, the value of [tex]\( f(g(5)) \)[/tex] is [tex]\( 21 \)[/tex].
Thus, the final answer is:
[tex]\[
f(g(5)) = 21
\][/tex]
