Given g(x)=
[6x for 0 < x < or = 2
[3x+3 for 2 < x < or = 8
[5x-4 for 8 < x < or = 12
Determine g(6)
Briefly explain
They should have also asked you to graph f(x), that would explain everything very nicely.
at g(6) the value of x falls in the domain
2 < x ≤ 8
so g(x) = 3x+3 for those values of x
then
f(6) = 3(6) + 3 = 21
whenever I typed f(x) above, it should have said g(x).
Thanks again!
To determine the value of g(6), we need to find the equation that applies to the given range of 6.
From the given function g(x), we can see that there are three different equations for different ranges of x.
For 0 < x ≤ 2, the equation is g(x) = 6x.
For 2 < x ≤ 8, the equation is g(x) = 3x + 3.
For 8 < x ≤ 12, the equation is g(x) = 5x - 4.
Since 6 falls within the range of 2 < x ≤ 8, we will use the equation g(x) = 3x + 3.
Now, substitute x = 6 into the equation:
g(6) = 3(6) + 3
= 18 + 3
= 21.
Therefore, g(6) = 21.