What is the value of f(-2 - g(3)) if f(x) = 3/4x + 10 and g(x) = x^2 - 3?

Understand the Problem

The question is asking us to calculate the value of the function f when it is evaluated at -2 minus the result of g evaluated at 3. This involves first calculating g(3), and then using that result in the function f.

Answer

The value of $f(-2 - g(3))$ is $4$.

Steps to Solve

Calculate g(3) We need to substitute 3 into the function $g(x) = x^2 - 3$.

[ g(3) = 3^2 - 3 = 9 - 3 = 6 ]

Evaluate -2 - g(3) Next, we substitute the value of $g(3)$ back into the expression $-2 - g(3)$.

[ -2 - g(3) = -2 - 6 = -8 ]

Calculate f(-8) Now, we substitute -8 into the function $f(x) = \frac{3}{4}x + 10$.

[ f(-8) = \frac{3}{4}(-8) + 10 = -6 + 10 = 4 ]

The value of $f(-2 - g(3))$ is $4$.

More Information

This problem involves evaluating two functions and combining their outputs. It's important to follow the order in which the computations are specified to avoid confusion.

Tips

Confusing the order of operations between the functions and miscalculating when substituting values.
Forgetting to apply the negative sign correctly when calculating $-2 - g(3)$.

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