The given function as;
f(x) = x² - 8x + 3
f(x + h) , susbtitute x = x + h in the given expression as;
f(x+h) = (x+h)² - 8(x+h) + 3
f(x+h) = (x² + h² + 2xh) -8x - 8h + 3
f(x+h) = x² + h² + 2xh - 8x - 8h + 3
Now substitute the value of f(x+h) in the expression as;
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{(x^2+h^2+2xh-8x-8h+3)-(x^2-8x+3)}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{x^2+h^2+2xh-8x-8h+3-x^2+8x-3}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{x^2-x^2+h^2+2xh-8x+8x-8h+3-3}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{2xh+h^2-8h}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{h(2x+h-8)}{h} \\ \frac{f(x+h)-f(x)}{h}=2x+h-8 \end{gathered}[/tex]
Answer : 2x + h - 8
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