Answer :
To solve the problem, let's break it down step-by-step.
1. Define the functions [tex]\( h(x) \)[/tex] and [tex]\( k(x) \)[/tex]:
[tex]\[ h(x) = x^2 - 3 \][/tex]
[tex]\[ k(x) = 5 + x \][/tex]
2. Calculate [tex]\( h(7) \)[/tex]:
We substitute [tex]\( x = 7 \)[/tex] into the function [tex]\( h(x) \)[/tex]:
[tex]\[ h(7) = 7^2 - 3 \][/tex]
Calculate [tex]\( 7^2 \)[/tex]:
[tex]\[ 7^2 = 49 \][/tex]
Then subtract 3:
[tex]\[ 49 - 3 = 46 \][/tex]
So, [tex]\( h(7) = 46 \)[/tex].
3. Calculate [tex]\( k(h(7)) \)[/tex], which is [tex]\( k(46) \)[/tex]:
We substitute [tex]\( x = 46 \)[/tex] into the function [tex]\( k(x) \)[/tex]:
[tex]\[ k(46) = 5 + 46 \][/tex]
Adding the numbers together:
[tex]\[ 5 + 46 = 51 \][/tex]
So, [tex]\( k(46) = 51 \)[/tex].
Therefore, the value of [tex]\( k(h(7)) \)[/tex] is [tex]\( 51 \)[/tex].
The correct answer is:
[tex]\[ \boxed{51} \][/tex]
1. Define the functions [tex]\( h(x) \)[/tex] and [tex]\( k(x) \)[/tex]:
[tex]\[ h(x) = x^2 - 3 \][/tex]
[tex]\[ k(x) = 5 + x \][/tex]
2. Calculate [tex]\( h(7) \)[/tex]:
We substitute [tex]\( x = 7 \)[/tex] into the function [tex]\( h(x) \)[/tex]:
[tex]\[ h(7) = 7^2 - 3 \][/tex]
Calculate [tex]\( 7^2 \)[/tex]:
[tex]\[ 7^2 = 49 \][/tex]
Then subtract 3:
[tex]\[ 49 - 3 = 46 \][/tex]
So, [tex]\( h(7) = 46 \)[/tex].
3. Calculate [tex]\( k(h(7)) \)[/tex], which is [tex]\( k(46) \)[/tex]:
We substitute [tex]\( x = 46 \)[/tex] into the function [tex]\( k(x) \)[/tex]:
[tex]\[ k(46) = 5 + 46 \][/tex]
Adding the numbers together:
[tex]\[ 5 + 46 = 51 \][/tex]
So, [tex]\( k(46) = 51 \)[/tex].
Therefore, the value of [tex]\( k(h(7)) \)[/tex] is [tex]\( 51 \)[/tex].
The correct answer is:
[tex]\[ \boxed{51} \][/tex]
