Let f(x) = x / (x-7) and g(x) = 3 / x

Find the function of f(g(x))

To find the function \( f(g(x)) \), we need to substitute \( g(x) \) into the function \( f(x) \).

Given:
\[
f(x) = \frac{x}{x - 7}
\]
\[
g(x) = \frac{3}{x}
\]

We substitute \( g(x) \) into \( f(x) \):

\[
f(g(x)) = f\left(\frac{3}{x}\right)
\]

Now, replace \( x \) in \( f(x) \) with \( \frac{3}{x} \):

\[
f(g(x)) = \frac{\frac{3}{x}}{\frac{3}{x} - 7}
\]

Next, simplify the expression:

\[
f(g(x)) = \frac{\frac{3}{x}}{\frac{3 - 7x}{x}}
\]

Simplify further:

\[
f(g(x)) = \frac{3/x}{(3 - 7x)/x} = \frac{3}{3 - 7x}
\]

So, the function \( f(g(x)) \) is:

\[
f(g(x)) = \frac{3}{3 - 7x}
\]

Would you like more details or have any questions about this process?

Here are some related questions:

1. How do you find the domain of \( f(g(x)) \)?
2. What is \( g(f(x)) \)?
3. How do you determine the inverse of \( f(x) \)?
4. What happens if \( x = 7 \) in \( f(x) \)?
5. How would you graph \( f(g(x)) \)?

**Tip:** When substituting functions, ensure all instances of the variable are replaced correctly to avoid mistakes.

Discover how to find the function f(g(x)) using function composition. Step-by-step solution provided for the functions f(x) = x / (x - 7) and g(x) = 3 / x. Suitable for high school students and anyone studying functions and composition.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation