College Algebra

Question

If f(x)=2x-1, h(fox)= -x-2 ; then find (f(h) 4

Answer 1

Hello, thank you for taking the time to post your question!

You’re given that f(x) = 2x – 1 and h(f(x)) = -x – 2 and then we’re trying to find the value of f(h(4))

There are a variety of ways to go about doing that but basically the idea here is that we need to flip the direction of the composite. I think the best approach to take is to first find the function h(x) with u-substitution … so that means that if we let u = f(x), then u = 2x – 1, meaning that x = (u + 1)/2

h(u) = -(u+1)/2 – 2

= -u/2 – ½ - 2

= -u/2 – 5/2

Which means that

h(x) = -x/2 – 5/2

from there then you can find h(4) directly by taking

h(4) = -4/2 -5/2 = -2 – 2.5 = -4.5

then the final step is using that intermediate value to find f(-4.5)

f(-4.5) = 2(-4.5) – 1 = -9 – 1 = -10

meaning that our end value here is f(h(4)) = -10

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

So we know the following

f(x) = 2x -1

h(f(x)) = -x -2

In order to find f(h(4)), we first need to know what is h(4) = h(f(x) = 4). In other words we want to find a value for x, that makes f(x) = 4 to plug it into h(f(x))

f(x) = 4

2x - 1= 4

x = 5/2

h(f(5/3)) = -5/2-2 = -7/2

So now we have h(4) = -7/2, so the last step is to find f(h(4)) = f(-7/2)

f(-7/2) = 2*(-7/2) -1

f(h(4)) = f(-7/2) = -8