Problem

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

Solution

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

From Solvely APP
Source: https://solvelyapp.com/problems/27468/

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