given that f(x)=5x-1 and G(x)=x squared + 4, what is f(g(6))

To find \( f(g(6)) \), we need to follow these steps:

### 1. Find \( g(6) \):
The function \( g(x) = x^2 + 4 \). 
Substitute \( x = 6 \) into the equation:

\[
g(6) = 6^2 + 4 = 36 + 4 = 40
\]

### 2. Use this result to find \( f(g(6)) \), which is \( f(40) \):
The function \( f(x) = 5x - 1 \). 
Now substitute \( x = 40 \) into the equation:

\[
f(40) = 5(40) - 1 = 200 - 1 = 199
\]

### Therefore, \( f(g(6)) = 199 \).

Would you like any additional details or clarifications?

Here are 5 related questions for further practice:
1. What is \( g(f(3)) \) given the same functions \( f(x) \) and \( g(x) \)?
2. Find the composition \( f(g(x)) \) in terms of \( x \).
3. What is the inverse of the function \( f(x) = 5x - 1 \)?
4. Calculate \( g(g(5)) \) for the given function \( g(x) \).
5. If \( h(x) = f(x) + g(x) \), what is \( h(6) \)?

**Tip:** When solving compositions of functions, always work from the inside out, evaluating the innermost function first.

Given that f(x) = 5x - 1 and g(x) = x^2 + 4, what is f(g(6))?

Learn how to solve the composition of functions problem f(g(6)) where f(x) = 5x - 1 and g(x) = x^2 + 4. This step-by-step solution covers core algebraic concepts such as function composition and quadratic expressions. Ideal for students in Grades 9-10.

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