Question 1)
Given the function
f(x) = 2|x+10| - 6
You need to remember that:
f(x) = y
f(0) means we need to determine the value of y at x = 0.
so substitute x = 0 in the function
[tex]f\left(x\right)\:=\:2|x+10|\:-\:6[/tex]
[tex]f\left(0\right)\:=\:2|0+10|\:-\:6[/tex]
[tex]=2\left|10\right|-6[/tex]
Apply absolute value: [tex]\left|a\right|=a,\:a\ge 0[/tex]
[tex]=2\cdot \:10[/tex]
[tex]=20[/tex]
Thus,
[tex]f\left(0\right)\:=\:20[/tex]
Question 2)
Given the fuction
g(x) = x+1
substitute g(x) = 20 in the function
20 = x+1
x = 20-1
x = 19
Thus,
x = 0
Question 3)
Given the function
f(x)=2|x+10|-6
substitute x = 1 in the function
f(1)=2|1+10|-6
f(1)=2|1+10|-6
f(1) = 2|11| - 6
Apply absolute value: [tex]\left|a\right|=a,\:a\ge 0[/tex]
f(1) = 2(11) - 6
f(1) = 22 - 6
f(1) = 16
Given the function
g(x)=x+1
substitute x = 0 in the function
g(0) = 0+1
g(0) = 1
Thus,
g(0)+f(1) = 16+1
= 17
