https://file.aiquickdraw.com/mathbot/file/1726187437290pyos3too.jpg

The image provides four functions:

1. \( m(x) = 5x - 3 \)
2. \( n(x) = x + 4 \)
3. \( c(x) = 5x^2 + 17x - 12 \)
4. \( t(x) = \frac{x - 5}{x + 2} \)

Would you like to evaluate these functions for specific values of \(x\), find compositions of functions, or explore another type of operation?

Here are 5 related questions for further exploration:
1. What is \( m(n(x)) \), the composition of \( m(x) \) and \( n(x) \)?
2. Find the roots of \( c(x) = 0 \).
3. What is the domain of \( t(x) \)?
4. Compute the derivative of \( c(x) \).
5. Evaluate \( t(3) \).

**Tip:** When combining functions (composition), always substitute the inner function first before simplifying.

Given the following functions: m(x) = 5x - 3, n(x) = x + 4, c(x) = 5x^2 + 17x - 12, t(x) = (x - 5) / (x + 2)

Explore the mathematical functions m(x) = 5x - 3, n(x) = x + 4, c(x) = 5x^2 + 17x - 12, and t(x) = (x - 5) / (x + 2). This problem covers key concepts such as function composition, solving quadratic equations, and domain restrictions in rational functions. Suitable for high school students in Grades 9-12.

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