Questions: If f(x)=2x and g(x)=4x^2, find (f+g)(x)= (f-g)(x)= (f * g)(x)= (f/g)(x)=, x ≠

Transcript text: If $f(x)=2 x$ and $g(x)=4 x^{2}$, find $(f+g)(x)=$ $\square$ $(f-g)(x)=$ $\square$ $(f \cdot g)(x)=$ $\square$ $\left(\frac{f}{g}\right)(x)=\square, x \neq$ $\square$

Solution

Solution Steps

Step 1: Understanding the Functions

We are given two functions:

$ f(x) = 2x $
$ g(x) = 4x^2 $

Step 2: Solving for $ (f+g)(x) $

To find $ (f+g)(x) $, we add the functions $ f(x) $ and $ g(x) $: \[ (f+g)(x) = f(x) + g(x) = 2x + 4x^2 \]

Step 3: Solving for $ (f-g)(x) $

To find $ (f-g)(x) $, we subtract $ g(x) $ from $ f(x) $: \[ (f-g)(x) = f(x) - g(x) = 2x - 4x^2 \]

Step 4: Solving for $ (f \cdot g)(x) $

To find $ (f \cdot g)(x) $, we multiply the functions $ f(x) $ and $ g(x) $: \[ (f \cdot g)(x) = f(x) \cdot g(x) = (2x) \cdot (4x^2) = 8x^3 \]

Final Answer

$(f+g)(x) = \boxed{2x + 4x^2}$
$(f-g)(x) = \boxed{2x - 4x^2}$
$(f \cdot g)(x) = \boxed{8x^3}$

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