Problem

Let $f(x)=7 x+6$ and $g(x)=4-x^{2}$. Evaluate the following: 1. $f(g(0))=$ 2. $g(f(0))=$

Solution

Step 1 :Define the functions: \(f(x) = 7x + 6\) and \(g(x) = 4 - x^2\).

Step 2 :For the first question, we are asked to evaluate \(f(g(0))\). This means we first evaluate \(g(0)\) and then substitute the result into \(f(x)\).

Step 3 :Evaluate \(g(0)\) to get 4.

Step 4 :Substitute 4 into \(f(x)\) to get \(f(4) = 7*4 + 6 = 34\).

Step 5 :So, \(f(g(0)) = \boxed{34}\).

Step 6 :For the second question, we are asked to evaluate \(g(f(0))\). This means we first evaluate \(f(0)\) and then substitute the result into \(g(x)\).

Step 7 :Evaluate \(f(0)\) to get 6.

Step 8 :Substitute 6 into \(g(x)\) to get \(g(6) = 4 - 6^2 = -32\).

Step 9 :So, \(g(f(0)) = \boxed{-32}\).

From Solvely APP
Source: https://solvelyapp.com/problems/7914/

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