The difference quotient for the function f(x) is [tex]h+2x-7[/tex]
Given :
Difference quotient formula
[tex]\frac{\left(f\left(x+h\right)-f\left(x\right)\right)}{h}[/tex]
Given function [tex]f(x) = x^2 - 7x + 8[/tex]
find the difference quotient using the formula
first we find out f(x+h) using given f(x)
replace x with x+h
[tex]f(x) = x^2 - 7x + 8 \\f(x+h)=\mathrm{ }\left(x+h\right)^2-7\left(x+h\right)+8\\Expand \; and \; simplify\\f(x+h)=x^2+2xh+h^2-7\left(x+h\right)+8\\f(x+h)=x^2+2xh+h^2-7x-7h+8[/tex]
Now replace it in our formula and also replace f(x)
[tex]\frac{\left(f\left(x+h\right)-f\left(x\right)\right)}{h}\\ \frac{x^2+2xh+h^2-7x-7h+8-(x^2 - 7x + 8)}{h} \\\frac{x^2+2xh+h^2-7x-7h+8-x^2 + 7x - 8}{h} \\\\\frac{h^2+2xh-7h}{h}\\factor \; out \; h\\\frac{h\left(h+2x-7\right)}{h}\\h+2x-7[/tex]
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