Question

What composition forms the equation p(x) when given the functions for h(x), f(x), k(x), and g(x)? PLEASE HELP!!!!! thank you!!!!! *will ofc give brainliest*

Answer 1

Answer:  Choice B.  k(h(g(f(x))))

For choice B, the functions are k, h, g, f going from left to right.

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Explanation:

We have 4x involved, so we'll need f(x)

This 4x term is inside a cubic, so we'll need g(x) as well.

So far we have

g(x) = x^3

g( f(x) ) = ( f(x) )^3

g( f(x) ) = ( 4x )^3

Then note how we are dividing that result by 2. That's the same as applying the h(x) function

$h(x) = \frac{x}{2}\\\\h(g(f(x))) = \frac{g(f(x))}{2}\\\\h(g(f(x))) = \frac{(4x)^3}{2}$

And finally, we subtract 1 from this, but that's the same as using k(x)

$k(x) = x-1\\\\k(h(g(f(x)))) = h(g(f(x)))-1\\\\k(h(g(f(x)))) = \frac{(4x)^3}{2}-1$

This leads to the answer choice B.

To be honest, this notation is a mess considering how many function compositions are going on. It's very easy to get lost. I recommend carefully stepping through the problem and building it up in the way I've done above, or in a similar fashion. The idea is to start from the inside and work your way out. Keep in mind that PEMDAS plays a role.