Questions: Use the given graph to evaluate the following expressions. (a) (f + g)(2) (b) (f - g)(1) (c) (fg)(0) (d) (f/g)(1)

Transcript text: Use the given graph to evaluate the following expressions. (a) $(\mathrm{f}+\mathrm{g})(2)$ (b) $(\mathrm{f}-\mathrm{g})(1)$ (c) $(\mathrm{fg})(0)$ (d) $\left(\frac{f}{g}\right)(1)$

Solution

Solution Steps

Step 1: Evaluate $ f(2) $ and $ g(2) $

From the graph:

$ f(2) = 0 $
$ g(2) = 2 $

Step 2: Calculate $ (f + g)(2) $

Using the values from Step 1: \[ (f + g)(2) = f(2) + g(2) = 0 + 2 = 2 \]

Step 3: Evaluate $ f(1) $ and $ g(1) $

From the graph:

$ f(1) = 1 $
$ g(1) = 1 $

Step 4: Calculate $ (f - g)(1) $

Using the values from Step 3: \[ (f - g)(1) = f(1) - g(1) = 1 - 1 = 0 \]

Step 5: Evaluate $ f(0) $ and $ g(0) $

From the graph:

$ f(0) = 2 $
$ g(0) = 0 $

Step 6: Calculate $ (fg)(0) $

Using the values from Step 5: \[ (fg)(0) = f(0) \cdot g(0) = 2 \cdot 0 = 0 \]

Final Answer

(a) $ (f + g)(2) = 2 $
(b) $ (f - g)(1) = 0 $
(c) $ (fg)(0) = 0 $

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!