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

Steps

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

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

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

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

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

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

Answer

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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.