*F as a function of g(x)*", or

**let x=g(x)**:

**same method**to solve for G(f(x)).

find (f @ g)(x) and (g @ f)(x) fo the indicated functions :

f(x) = 6x - 7, g(x) = x + 7

6

(f @ g)(x) = ?

(g @ f)(x) = ?

simplify your answers

Tutors, sign in to answer this question.

Krystal S. | Patient, Fun, and Well-Rounded TutorPatient, Fun, and Well-Rounded Tutor

Hi Keith!

When you see problems like (f@g)(x), read it as
f(g(x)). The problem tells you what
f(x) and g(x) are, therefore f(g(x)) means you're taking x of the given f(x) equation and substituting the x for g(x).

(F@g)(x) means "Instead of the usual F(x), which reads "F as a function of x", you'll solve for
*F as a function of g(x)*", or
**let x=g(x)**:

F(x)=6x-7 and
G(x)=(x+7)/6 …so…
F(g(x))=6[(x+7)/6]-7

Now, distribute what you have on the right side of the equation (which I'll let you do on your own), and you'll have your answer!

Now, for the second half of this problem, use this **same method** to solve for
G(f(x)).

**Important Note: With this problem, F(g(x)) and G(f(x)) just happen to be the same, but this is
not a typical case! Make sure you do the work on both parts of the problem.

I find color coding really helps some people when working on these types of problems, like I used in my answer. I hope this helps you, and let me know if I can help you with anything else.

Good luck on the rest of your assignment :)

Hi again Keith;

f(x)=6x-7

f(g(x))={(6)[(x+7)/6]}-7

The 6 in both the numerator and denominator cancels...

f(g(x))=(x+7)-7

f(g(x))=x

g(x)=(x+7)/6

g(f(x))=[(6x-7)+7]/6

g(f(x))=(6x-7+7)/6

g(f(x))=6x/6

g(f(x))=x

While we have identical results herein, this is not typical of f(g(x)) and g(f(x)). Please do not always expect such.

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Evan G.

Math Help and Test Prep with a National Merit Scholar!

$7.50 per 15 min

View Profile >

Vincent L.

History, Social Studies, English, and Test Prep tutor

$10 per 15 min

View Profile >

Jennifer N.

Middle, high school, college & adult math tutor

$10 per 15 min

View Profile >