Questions: Use f(x)=3x-2 and g(x)=5-x^2 to evaluate the expression. (a) f(f(2)) (b) g(g(3))

Solution Steps

To solve the given problems, we need to evaluate the functions $f(x)$ and $g(x)$ using the provided expressions.

(a) For $f(f(2))$, first calculate $f(2)$ using the function $f(x) = 3x - 2$. Then, use the result to find $f$ of that result.

(b) For $g(g(3))$, first calculate $g(3)$ using the function $g(x) = 5 - x^2$. Then, use the result to find $g$ of that result.

To find $f(f(2))$, we first need to evaluate $f(2)$ using the function $f(x) = 3x - 2$.

$$f(2) = 3(2) - 2 = 6 - 2 = 4$$

Now, use the result from Step 1 to find $f(f(2))$.

$$f(f(2)) = f(4) = 3(4) - 2 = 12 - 2 = 10$$

To find $g(g(3))$, we first need to evaluate $g(3)$ using the function $g(x) = 5 - x^2$.

$$g(3) = 5 - 3^2 = 5 - 9 = -4$$

Now, use the result from Step 3 to find $g(g(3))$.

$$g(g(3)) = g(-4) = 5 - (-4)^2 = 5 - 16 = -11$$

Final Answer