If `f(x)=2x^(2)+7x-9 and g(x)=2x+3`, then find the vlaue of `g(g(x))` at `x=2`

Options

A. 92
B. 39
C. 29
D. none of these

Answer

To find the value of \( g(g(x)) \) at \( x = 2 \), we will follow these steps:

### Step 1: Calculate \( g(2) \)
Given the function \( g(x) = 2x + 3 \), we first need to find \( g(2) \).

\[ g(2) = 2(2) + 3 \]
\[ g(2) = 4 + 3 = 7 \]

### Step 2: Calculate \( g(g(2)) \)
Now, we need to find \( g(g(2)) \), which is \( g(7) \).

Using the function \( g(x) = 2x + 3 \):

\[ g(7) = 2(7) + 3 \]
\[ g(7) = 14 + 3 = 17 \]

### Final Answer
Thus, the value of \( g(g(2)) \) is \( 17 \).

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