solve this problem step by step---Let $f(x) = \frac{3}{4}x + 10$,
$g(x) = x^2 - 3$.
What is the value of $f(-2 - g(3))$?
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We have two functions: f of x equals three-fourths x plus ten, and g of x equals x squared minus three. We need to find the value of f of negative two minus g of three.
First, we need to evaluate g of 3. We substitute x equals 3 into the function g of x equals x squared minus 3. This gives us g of 3 equals 3 squared minus 3, which equals 9 minus 3, which equals 6.
Now we calculate the argument of function f. We need to find negative 2 minus g of 3. Since g of 3 equals 6, we have negative 2 minus 6, which equals negative 8. So we need to evaluate f of negative 8.
Now we evaluate f of negative 8. We substitute x equals negative 8 into the function f of x equals three-fourths x plus 10. This gives us f of negative 8 equals three-fourths times negative 8 plus 10, which equals negative 6 plus 10, which equals 4.
To summarize our solution: First, we evaluated g of 3 which equals 6. Then we calculated negative 2 minus g of 3, which equals negative 8. Finally, we evaluated f of negative 8, which equals 4. Therefore, f of negative 2 minus g of 3 equals 4.