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Answer:

[tex]\large{\boxed{\sf 2x+h-4}}[/tex]

Explanation:

f(x) = x² - 4x + 3

f(x + h) = (x + h)² - 4(x + h) + 3

Solving Steps:

[tex]\rightarrow \sf \dfrac{(x + h)^2 - 4(x + h) + 3 - (x^2 - 4x + 3)}{h}[/tex]

[tex]\rightarrow \sf \dfrac{x^2 + 2xh + h^2 - 4x -4h+3-x^2+4x-3}{h}[/tex]

[tex]\sf \rightarrow \dfrac{2xh+h^2-4h}{h}[/tex]

[tex]\rightarrow \sf 2x+h-4[/tex]
  • f(x)=x²-4x+3
  • f(x+h)=(x+h)²-4(x+h)+3=x²+2xh+h²-4x-4h+3

Put values

[tex]\\ \rm\Rrightarrow \dfrac{x^2+2xh+h^2-4x-4h+3-x^2+4x-3}{h}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{2xh+h^2-4h}{h}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{h(2x+h-4)}{h}[/tex]

[tex]\\ \rm\Rrightarrow 2x+h-4[/tex]

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