Problem

Consider the function f(x)=x2+5
Use it to find f(4),f(3), and f(a3)

Answer

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Answer

The final results are in their simplest form, and they meet the requirements of the problem.

Steps

Step 1 :First, we need to understand the function f(x)=x2+5. This is a quadratic function, where x is the variable, and x2+5 is the expression that gives the value of the function for any given x.

Step 2 :To find f(4), we substitute x=4 into the function: f(4)=42+5=16+5=11.

Step 3 :To find f(3), we substitute x=3 into the function: f(3)=(3)2+5=9+5=4.

Step 4 :To find f(a3), we substitute x=a3 into the function: f(a3)=(a3)2+5=(a26a+9)+5=a2+6a4.

Step 5 :So, f(4)=11, f(3)=4, and f(a3)=a2+6a4.

Step 6 :We can check our results by substituting the values back into the original function and verifying that they satisfy the equation.

Step 7 :The final results are in their simplest form, and they meet the requirements of the problem.

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