2.)If f(x)=3x,g(x)=x-3,and h(x)= the square root of x, find (fogox)(X). I really didn't get this will someone please show me how to do it?
This I what I did to solve for it:
3(x-3)
3(he square root of 25-3
3(5-3)
15-9=6
Ok here is another way I solved for it but I am still not sure if I am doing any of the work right.
f(g(h))(25)
f(g(square root of f(x)))(25)
f(g(1.7))(25)
f(1.7-3)
F(-1.3)
f(25)=3(25)
f(25)=75
Which one is correct and if they are both wrong will you help me get the right answer and understand how to do it?
To find (f o g o h)(x), we need to substitute the functions into each other in the correct order. Let's break it down step by step.
First, let's find f(g(x)) using g(x) = x - 3:
f(g(x)) = f(x - 3)
Next, let's find f(g(x)) using f(x) = 3x:
f(g(x)) = 3(x - 3)
Now, let's find f(g(h(x))) using h(x) = sqrt(x):
f(g(h(x))) = f(g(sqrt(x)))
Finally, let's substitute x with 25 into f(g(h(x))) to find (f o g o h)(25):
(f o g o h)(25) = f(g(sqrt(25)))
Now, let's solve this step by step using the correct order:
1. Start with h(x) = sqrt(x):
h(25) = sqrt(25) = 5
2. Next, use g(x) = x - 3:
g(h(25)) = g(5) = 5 - 3 = 2
3. Finally, use f(x) = 3x:
f(g(h(25))) = f(2) = 3 * 2 = 6
Therefore, (f o g o h)(25) = 6.
So, the correct answer is 6. Your first attempt was close, but there was a mistake when you squared 25 inside the square root. Remember that the square root of 25 is 5, not 25 itself. Your second attempt seems to have the wrong order of function composition.
I hope this explanation helps!