Given $f (x) = 4 x - 2$
(a) Find $f (x + h)$ and simplify.
(b) Find $\frac{f (x + h) - f (x)}{h}$ and simplify.

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$Final Answer: (a) f (x + h) = 4 h + 4 x - 2, (b) \frac{f (x + h) - f (x)}{h} = 4$

Steps

Step 1 ：Substitute $x + h$ into the function $f (x) = 4 x - 2$ to get $f (x + h) = 4 (x + h) - 2$

Step 2 ：Simplify $f (x + h)$ to get $f (x + h) = 4 h + 4 x - 2$

Step 3 ：Substitute $x + h$ and $x$ into the function $f (x)$ , subtract the two results, and then divide by $h$ to get $\frac{f (x + h) - f (x)}{h} = \frac{(4 h + 4 x - 2) - (4 x - 2)}{h}$

Step 4 ：Simplify $\frac{f (x + h) - f (x)}{h}$ to get $\frac{f (x + h) - f (x)}{h} = 4$

Step 5 ： $Final Answer: (a) f (x + h) = 4 h + 4 x - 2, (b) \frac{f (x + h) - f (x)}{h} = 4$

Given f(x)=4x−2(a) Find f(x+h) and simplify.(b) Find f(x+h)−f(x)h and simplify.

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Given $f (x) = 4 x - 2$
(a) Find $f (x + h)$ and simplify.
(b) Find $\frac{f (x + h) - f (x)}{h}$ and simplify.