I need help with this question.
Suppose that f(0)= 0 , f(1)= 4, f(2)= 4, f(3)= 10, f(4)= 16 and g(x) = -f(2x+3). Find any 5 points on g(x).
if x = -1, 2x+3 = 1 and -f(1) = -4
if x = 0, 2x+3 = 3 and -f(3) = -10
etc
you have f for 0,1,2,3,4
Clearly, since
g(x) = -f(2x+3)
g(-3/2) = -f(0) = 0 so (-3/2,0)
g(-1) = -f(1) = -4 so (-1,-4)
and so on
I still don't understand.
Steve and I both said the same thing in different ways. Here is another.
like when is 2x+3 = 0 ???
when x = -3/2
so what is f(0)
it is 0
so when x = -3/2 then g(x) = 0
ok tell me if i did this question correct. I just worked out the question.
-f(0) =(-3/2, 0)
-f(1) =(-1, -4)
-f(2) =(-1/2, -4)
-f(3) =(0 , -10)
-f(4) =(1/2, -16)
looks good to me.
To find the values of g(x), we can use the given function g(x) = -f(2x+3) and substitute different values of x into it.
1. Find g(0):
Substituting x = 0 into g(x) = -f(2x+3):
g(0) = -f(2(0)+3) = -f(3) = -10
Therefore, g(0) = -10.
2. Find g(1):
Substituting x = 1 into g(x) = -f(2x+3):
g(1) = -f(2(1)+3) = -f(5) = ??? (We do not have the value of f(5) given in the question.)
3. Find g(2):
Substituting x = 2 into g(x) = -f(2x+3):
g(2) = -f(2(2)+3) = -f(7) = ??? (We do not have the value of f(7) given in the question.)
4. Find g(3):
Substituting x = 3 into g(x) = -f(2x+3):
g(3) = -f(2(3)+3) = -f(9) = ??? (We do not have the value of f(9) given in the question.)
5. Find g(4):
Substituting x = 4 into g(x) = -f(2x+3):
g(4) = -f(2(4)+3) = -f(11) = ??? (We do not have the value of f(11) given in the question.)
Unfortunately, without the values of f(5), f(7), f(9), and f(11), we cannot find the exact values of g(1), g(2), g(3), and g(4) as requested in the question.