Given f(x) and h(x) find g(x) so that f(g(x)) = h(x)
f(x) = x+4
h(x) = 4x-1
So far I have determined that g(x+4) = 4x-1 but am baffled as to how you determine g(x). Seems like a simple problem but I'm having a bit of a problem on it. Please show work!!
2007-09-04 08:25:02 · 9 answers · asked by drew2007 1 in Science & Mathematics ➔ Mathematics
Typo on the original question. I need to find it when g(f(x)) = h(x) not the other way around.
2007-09-04 08:38:41 · update #1
Typo on the original question. I need to find it when g(f(x)) = h(x) not the other way around.
2007-09-04 08:38:43 · update #2
f(x) is linear , so f(g(x)) = g(x) + 4 = 4x - 1, and g(x) = 4x - 5
Test this:
f(4x-5) = 4x -5 + 4 = 4x - 1 -- ok!
2007-09-04 08:31:55 · answer #1 · answered by John V 6 · 0⤊ 0⤋
First we have to start with a definition of the composition of functions: Combining two functions by substituting one function's formula in place of each x in the other function's formula. The composition of functions f and g is written f ° g, and is read aloud "f composed with g." The formula for f ° g is written (f ° g)(x). This is read aloud "f composed with g of x."
Now in order for f(g(x)) to meet the above definition, we will have to find a function to serve as a value of x to make f(x) = h(x).
x+4 = 4x-1, true? No, so we'll have to change it around a bit.
Ok, if we're going to substitute something for x on the left side of the equation, we can see that it's going to have to have its own "x" to make up for it, let's write that down somewhere.... g(x) = (?x+/-?)
We also see that it needs to be multiplied by 4 so g(x) = (4x+/-?)
We can also tell that -1 is smaller than 4, so...g(x) = (4x-?)Now we have to find out what number we can subtract from the "4" on the left side to come up with the "-1" on the right side, we can find this number by finding the difference between 4 and -1. 4 minus negative 1 produces a double negative, making it a positive, so the problem becomes four plus 1, which = 5. So...g(x) = (4x-5), if we put this equation in the place of the x in f(x) = h(x) we have the equation
(4x-5)+4=4x-1, to simplify the left side, we'll go ahead and add the 4 to -5.
So... 4x -1 = 4x - 1, true? Yes. So we have properly solved the problem! :):):)
2007-09-04 08:45:10 · answer #2 · answered by Rose 2 · 0⤊ 0⤋
Given f(x) and h(x) find g(x) so that f(g(x)) = h(x)
f(x) = x+4
h(x) = 4x-1
g(x) = 4x-5
f(g(x)) = 4x-5+4 = 4x-1 = h(x)
2007-09-04 08:32:29 · answer #3 · answered by ironduke8159 7 · 0⤊ 0⤋
f(g(x)) = g(x) + 4, g(x) + 4 = 4x - 1, g(x) = 4x - 5. Check: f(4x-5) = (4x - 5) + 4 = 4x - 1 = h(x)
2007-09-04 08:30:07 · answer #4 · answered by Marvin 4 · 0⤊ 0⤋
a million) finished fee = (style of months * consistent with month fee) + setting up fee finished fee = y style of months = x y = 30x + 50 2) putting y = 230 230 = 30x + 50 30x = 230 - 50 = a hundred and eighty x = a hundred and eighty/30 = 6 for this reason finished fee could be $230 in 6 months
2016-10-17 22:48:54 · answer #5 · answered by Anonymous · 0⤊ 0⤋
Plug in g(x) for x in f(x).
g(x) + 4 = 4x-1
g(x) = 4x-5
2007-09-04 08:31:48 · answer #6 · answered by Deborah P 2 · 0⤊ 0⤋
I think this is how you would do it!
F(X) = X + 4
H(X) = 4x – 1
F(G(X)) = H(X)
G(X) + 4 = 4X – 1
G(X) = 4X – 1 – 4
G(X) = 4X -5
2007-09-04 08:31:12 · answer #7 · answered by stylez-M 2 · 0⤊ 0⤋
g(x) = 4x-17
i already answered it in detail in another post.. look for it. in my profile
2007-09-04 09:11:18 · answer #8 · answered by vek14 3 · 0⤊ 0⤋
are you sure there isn't any more? you need a g(x) function
2007-09-04 08:40:34 · answer #9 · answered by computer whiz 5 · 0⤊ 0⤋