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