Questions: Using the function, f(x)=2-x, find the following: (a) f(x+h) (b) f(x+h)-f(x) (c) (f(x+h)-f(x))/h

Using the function, f(x)=2-x, find the following: (a) f(x+h) (b) f(x+h)-f(x) (c) (f(x+h)-f(x))/h
Transcript text: Using the function, $f(x)=2-x$, find the following: (a) $f(x+h)$ (b) $f(x+h)-f(x)$ (c) $\frac{f(x+h)-f(x)}{h}$
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Solution

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Solution Steps

Step 1: Finding $f(x+h)$

To find $f(x+h)$, substitute $x+h$ into $f(x)$: $f(x+h) = - h - x + 2$. Rounded: $-h - x + 2$.

Step 2: Finding $f(x+h) - f(x)$

The difference $f(x+h) - f(x)$ is calculated as: $- h$. Rounded: $-h$.

Step 3: Finding the Difference Quotient $\frac{{f(x+h) - f(x)}}{{h}}$

The difference quotient is: $-1$. Rounded: $-1$.

Final Answer:

$f(x+h)$ Rounded: $-h - x + 2$, $f(x+h) - f(x)$ Rounded: $-h$, Difference Quotient Rounded: $-1$.

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