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

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, please sign in to answer this question.

Stratford, CT

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 :)

Middletown, CT

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.

Nikunj P.

Math and Science Specialist, Over 14 Years of Educational Experience

Scarsdale, NY

4.9
(101 ratings)

Ari F.

Professional SAT/ACT Tutoring by former SAT Classroom Instructor

Teaneck, NJ

5.0
(162 ratings)

Avital S.

Patient tutor, for all ages, helps when your learning is blocked

Westwood, NJ

5.0
(505 ratings)

- Algebra 4067
- Algebra 1 3255
- Math Help 4200
- Algebra 2 2866
- Algebra Word Problem 2056
- Math 7260
- Math Help For College 1215
- Algebra Equation 300
- College Algebra 845
- Algebra Question 197