Let f(x) = 2x-3 and g(x) = 4x, find (fog)(x).

Answer: Question 4

To find \( (f \circ g)(x) \), also written as \( f(g(x)) \), you need to substitute \( g(x) \) into \( f(x) \). Here's the step-by-step process:

1. \( f(x) = 2x - 3 \)
2. \( g(x) = 4x \)

Now, find \( f(g(x)) \), which means we will substitute \( g(x) = 4x \) into \( f(x) \).

\[
f(g(x)) = f(4x)
\]

Substitute \( 4x \) into the expression for \( f(x) \):

\[
f(4x) = 2(4x) - 3 = 8x - 3
\]

Thus, \( (f \circ g)(x) = 8x - 3 \).

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Would you like more details on this process, or do you have any other questions?

Here are 5 related questions for further exploration:

1. What is \( (g \circ f)(x) \) for the same functions?
2. How do you find the inverse of \( f(x) \) and \( g(x) \)?
3. What is the domain and range of \( (f \circ g)(x) \)?
4. How do you compose three functions, like \( (h \circ g \circ f)(x) \)?
5. How does the composition of functions affect their derivatives in calculus?

**Tip:** Always check the domain of the inner function when performing compositions, as this can affect the domain of the overall composition.

Let f(x) = 2x - 3 and g(x) = 4x, find (fog)(x).

Learn how to find the composition of two functions, f(x) = 2x - 3 and g(x) = 4x, in this algebra problem. We demonstrate the step-by-step process to solve (f ∘ g)(x), focusing on key concepts like function composition. Suitable for students in Grades 9-11.

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