Suppose
[tex]f(x) = x^2 + 2x + 1,[/tex]
and
[tex]g(x) = x + 3.[/tex]
Find the value of
[tex]f(g(2)) - g(f(2)).[/tex]
Show all steps of your solution and explain any key concepts used in solving the problem.
[tex]f(x) = x^2 + 2x + 1,[/tex]
and
[tex]g(x) = x + 3.[/tex]
Find the value of
[tex]f(g(2)) - g(f(2)).[/tex]
Show all steps of your solution and explain any key concepts used in solving the problem.
Answers & Comments
Answer:
24
Step-by-step explanation:
so,
g(2)= 2+3=5
f(2)=4+4+1=9
f(5)=25+10+1=36
g(9)=9+3=12
f(g(2)) - g(f(2))= 36 -12 = 24
Verified answer
Solution :
Given, f(x) = x² + 2x + 1
g(x) = x + 3
We have to find value of f(g(2)) - g(f(2))
Firstly,
→ g(2) = 2 + 3
→ g(2) = 5
And, f(g(2)) = f(5)
→ f(5) = 5² + 2 × 5 + 1
→ f(5) = 25 + 10 + 1
→ f(5) = 36
Again, f(2) = 2² + 2 × 2 + 1
→ f(2) = 4 + 4 + 1
→ f(2) = 9
So, g(f(2)) = g(9)
→ g(9) = 9 + 3
→ g(9) = 12
Therefore,
→ f(g(2)) - g(f(2)) = 36 - 12
→ f(g(2)) - g(f(2)) = 24. (Ans.)