Questions: Let g(x)=3x and h(x)=x-2. Find the following. (g+h)(1/5)

Let g(x)=3x and h(x)=x-2. Find the following. (g+h)(1/5)
Transcript text: Let $g(x)=3 x$ and $h(x)=x-2$. Find the following. \[ (g+h)\left(\frac{1}{5}\right) \]
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Solution

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Solution Steps

To solve this problem, we need to find the sum of the functions \( g(x) \) and \( h(x) \) evaluated at \( x = \frac{1}{5} \). First, we will define the functions \( g(x) \) and \( h(x) \). Then, we will compute \( g\left(\frac{1}{5}\right) \) and \( h\left(\frac{1}{5}\right) \). Finally, we will add these two results together.

Step 1: Define the Functions

Given the functions \( g(x) = 3x \) and \( h(x) = x - 2 \).

Step 2: Evaluate the Functions at \( x = \frac{1}{5} \)

First, we evaluate \( g\left(\frac{1}{5}\right) \): \[ g\left(\frac{1}{5}\right) = 3 \cdot \frac{1}{5} = \frac{3}{5} \]

Next, we evaluate \( h\left(\frac{1}{5}\right) \): \[ h\left(\frac{1}{5}\right) = \frac{1}{5} - 2 = \frac{1}{5} - \frac{10}{5} = -\frac{9}{5} \]

Step 3: Sum the Results

Now, we sum the results of \( g\left(\frac{1}{5}\right) \) and \( h\left(\frac{1}{5}\right) \): \[ (g + h)\left(\frac{1}{5}\right) = g\left(\frac{1}{5}\right) + h\left(\frac{1}{5}\right) = \frac{3}{5} + \left(-\frac{9}{5}\right) = \frac{3}{5} - \frac{9}{5} = -\frac{6}{5} \]

Final Answer

\[ \boxed{ -\frac{6}{5} } \]

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