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Perform the given operation on $$  $$functions. Let h (×)= 1/4×+1 and g(×)=1/×,find g (h(×)).

The image you uploaded contains the mathematical problem that you typed earlier. I have already provided the solution for the given operation $ g(h(x)) $ based on the functions:

\[
h(x) = \frac{1}{4}x + 1 \quad \text{and} \quad g(x) = \frac{1}{x}
\]

The result for $ g(h(x)) $ is:

\[
g(h(x)) = \frac{1}{\frac{1}{4}x + 1}
\]

This is the simplified expression for $ g(h(x)) $.

Would you like any further details on this problem, or do you have any additional questions?

Here are 5 related questions:
1. How can we simplify the expression $ g(h(x)) = \frac{1}{\frac{1}{4}x + 1} $ further?
2. What is the domain and range of the function $ g(h(x)) $?
3. How would $ g(h(x)) $ behave as $ x $ approaches positive or negative infinity?
4. Can you find $ h(g(x)) $ for the given functions $ h(x) $ and $ g(x) $?
5. What is the significance of the composition of functions in calculus?

**Tip:** Understanding how to compose functions is crucial when solving complex mathematical problems, especially in calculus and algebra.

Explore the composition of functions g(h(x)) = 1 / (1/4x + 1). Learn how to apply function composition, analyze the domain and range, and understand its behavior as x approaches infinity. Suitable for high school students and anyone interested in calculus and algebra.

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