Let f(x)=1x-3 and g(x)=7x+3.


Find the following functions. Simplify your answers.


f(g(x))=    ,


g(f(x))=    .

We are given two functions:
- \( f(x) = 1x - 3 \)
- \( g(x) = 7x + 3 \)

Now, let's find the compositions of the functions.

### 1. Finding \( f(g(x)) \):

To compute \( f(g(x)) \), we substitute \( g(x) = 7x + 3 \) into \( f(x) = 1x - 3 \):
\[
f(g(x)) = f(7x + 3) = 1(7x + 3) - 3
\]
Simplify:
\[
f(g(x)) = 7x + 3 - 3 = 7x
\]

Thus, \( f(g(x)) = 7x \).

### 2. Finding \( g(f(x)) \):

To compute \( g(f(x)) \), we substitute \( f(x) = 1x - 3 \) into \( g(x) = 7x + 3 \):
\[
g(f(x)) = g(1x - 3) = 7(1x - 3) + 3
\]
Simplify:
\[
g(f(x)) = 7x - 21 + 3 = 7x - 18
\]

Thus, \( g(f(x)) = 7x - 18 \).

### Final Answers:
- \( f(g(x)) = 7x \)
- \( g(f(x)) = 7x - 18 \)

Would you like more details or explanations?

Here are some related questions:
1. What is the inverse of \( f(x) \) and \( g(x) \)?
2. Can you find \( f(f(x)) \) and \( g(g(x)) \)?
3. What happens if you solve \( f(x) = g(x) \)?
4. What are the domain and range of \( f(x) \) and \( g(x) \)?
5. How would you graph \( f(x) \) and \( g(x) \)?

**Tip:** Function compositions are useful for combining multiple transformations in algebra.

Let f(x)=1x-3 and g(x)=7x+3. Find the following functions. Simplify your answers. f(g(x))= , g(f(x))= .

Learn how to solve function compositions involving f(x)=1x-3 and g(x)=7x+3. This problem guides you through the steps to find f(g(x)) and g(f(x)) with simplified answers. Suitable for students in Grades 9-10.

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