Questions: Find (f-g)(x) for f(x)=x^2+8x and g(x)=3x+5.

Transcript text: Find $(f-g)(x)$ for $f(x)=x^{2}+8 x$ and $g(x)=3 x+5$.

Solution

Solution Steps

To find $(f-g)(x)$, we need to subtract the function $g(x)$ from the function $f(x)$. This involves subtracting the expressions for $g(x)$ from $f(x)$ and simplifying the resulting expression.

Step 1: Define the Functions

We have the functions defined as follows: \[ f(x) = x^2 + 8x \] \[ g(x) = 3x + 5 \]

Step 2: Calculate $(f-g)(x)$

To find $(f-g)(x)$, we compute: \[ (f-g)(x) = f(x) - g(x) = (x^2 + 8x) - (3x + 5) \] Simplifying this expression: \[ (f-g)(x) = x^2 + 8x - 3x - 5 = x^2 + 5x - 5 \]

Step 3: Evaluate $(f-g)(2)$

Now, we substitute $x = 2$ into the expression we derived: \[ (f-g)(2) = 2^2 + 5(2) - 5 \] Calculating this gives: \[ (f-g)(2) = 4 + 10 - 5 = 9 \]