Answer:
[tex]\textsf{1.} \quad f(x)+g(x) =8x^2+2x+3[/tex]
[tex]\textsf{2.} \quad f(x)-g(x)=-2x+1[/tex]
[tex]\textsf{3.} \quad h(x)+g(x)= 4x^2-x+5[/tex]
[tex]\textsf{4.} \quad h(x)-f(x)= -4x^2-3x+2[/tex]
[tex]\textsf{5.} \quad g(2)+f(x)= 4x^2+23[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=4x^2+2\\g(x)=4x^2+2x+1\\h(x)=-3x+4\end{cases}[/tex]
Function composition is an operation that takes two functions and produces a third function.
Question 1
Add function f(x) and function g(x) together:
[tex]\begin{aligned} \implies f(x)+g(x) & = (4x^2+2)+(4x^2+2x+1)\\& = 4x^2+2+4x^2+2x+1\\& = 4x^2+4x^2+2x+2+1\\& =8x^2+2x+3\end{aligned}[/tex]
Question 2
Subtract function g(x) from function f(x):
[tex]\begin{aligned} \implies f(x)-g(x) & = (4x^2+2)-(4x^2+2x+1)\\& = 4x^2+2-4x^2-2x-1\\& = 4x^2-4x^2-2x+2-1\\& =-2x+1\end{aligned}[/tex]
Question 3
Add function h(x) and function g(x) together:
[tex]\begin{aligned} \implies h(x)+g(x) & = (-3x+4)+(4x^2+2x+1)\\& = -3x+4+4x^2+2x+1\\& = 4x^2-3x+2x+4+1\\& = 4x^2-x+5\end{aligned}[/tex]
Question 4
Subtract function f(x) from function h(x):
[tex]\begin{aligned} \implies h(x)-f(x) & = (-3x+4)-(4x^2+2)\\ & = -3x+4-4x^2-2\\ & = -4x^2-3x+4-2\\ & = -4x^2-3x+2\end{aligned}[/tex]
Question 5
Add function g(x) when x = 2 to function f(x):
[tex]\begin{aligned} \implies g(2)+f(x) & = \left(4(2)^2+2(2)+1\right)+(4x^2+2)\\& = 4(4)+2(2)+1+4x^2+2\\& = 16+4+1+4x^2+2\\& = 4x^2+16+4+1+2\\& = 4x^2+23\end{aligned}[/tex]
Learn more about composite functions here:
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