A community for students.
Here's the question you clicked on:
 0 viewing
Atkinsoha
 3 years ago
If f(x) = (√x8) and g(x) =x+4, find the function h(x) such that h(x)= (f o g)^1. Be sure to give a domain restriction if necessary.
Need to know how to get the answer as well because I have to show work. Really lost. Help?
Atkinsoha
 3 years ago
If f(x) = (√x8) and g(x) =x+4, find the function h(x) such that h(x)= (f o g)^1. Be sure to give a domain restriction if necessary. Need to know how to get the answer as well because I have to show work. Really lost. Help?

This Question is Closed

Mathmuse
 3 years ago
Best ResponseYou've already chosen the best response.0If an equation is a function of x it means that when you sub in a value for x you'll get another value, the function value, 'out' of the function. When an equation is a function of another function, this means that the inner function will take on values as x changes, and this in turn will affect the outer function. take the example above, you have: h(x)  h is a function that varies as x changes g(x)  g is a function that varies as x changes f(x)  f is a function that varies as x changes (f o g) denotes that you first have to sub an x value into g, get the result and sub that into the variable for the function f. Let's break down your question: \[(f \space o\space g)=f(g(x))=f(x+4)\] so now where ever you see an x in the f(x) function you'll need to replace it with [x+4] \[(f\space o\space g) = f(x+4) = \sqrt{x+4}8\]

Mathmuse
 3 years ago
Best ResponseYou've already chosen the best response.0now you have a compound function, let's introduce the inverse and consider restrictions: \[(f\space o\space g)^{1}=\frac{1}{\sqrt{x+4}8}\] restrictions state that you can't have values less than zero under a root sign, so: \[x + 4 \ge 0\] \[x\ge 4\] But we also can't ever divide by zero so the denominator must be greater than zero: \[\sqrt{x+4}8\ne0\] \[\sqrt{x+4} \neq 8\] \[x+4 \neq 64\] \[x\neq 60\] since the domain must adhere to both these restrictions you must form a union with them: \[\left\{ x \in \mathbb{R} x \ge4, x\neq 60\right\}\]
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.