SOLUTION: Let f(x)=x^3 , g(x)=sqrt(x) , h(x)=x−4, and j(x)=2x. Express each function k as a composite of three of these four functions: k(x)=sqrt((x−4)^3)

Algebra ->  Functions -> SOLUTION: Let f(x)=x^3 , g(x)=sqrt(x) , h(x)=x−4, and j(x)=2x. Express each function k as a composite of three of these four functions: k(x)=sqrt((x−4)^3)       Log On


   

Question 1118012: Let f(x)=x^3 , g(x)=sqrt(x) , h(x)=x−4, and j(x)=2x. Express each function k as a composite of three of these four functions:
k(x)=sqrt((x−4)^3)
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Starting from the outside,
g%28f%28h%28x%29%29%29
g%28f%28x-4%29%29
g%28%28x-4%29%5E3%29
k%28x%29=sqrt%28%28x-4%29%5E3%29


Working from the inside, outward usually better to do.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Working from the outside as the other tutor did is one perfectly good way to find the answer.

I find it easier to work from the inside out. My thinking is as if I am evaluating the expression sqrt%28%28x-4%29%5E3%29%29.

The first thing you would do to evaluate the expression for a given value of x is subtract 4. So the innermost function is h(x) = x-4.

The next thing you would do is raise the result to the third power; so the next function (working out from the middle) is f(x) = x^3.

And the last thing you would do to evaluate the function is take the square root of the previous result; so the last (outermost) function is g(x) = sqrt(x).

So the correct composition of functions is g(f(h(x))).

If you don't work from the outside in, as the other tutor did, or from the inside out, as shown above, then you would have to start somewhere in the middle. That would probably be a path to failure.

So try both methods on other problems like this that you encounter and find which method works best for you.