Question

if f(x)=x²+2x-1 find f(x+1) and verify that f(x+1) - f(x)=2x+3

Answer 1

$\textbf {Hey there, here is the solution.}$
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f(x)=x²+2x-1 (Given)

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Find f(x + 1):

f(x + 1) = (x + 1)² + 2 (x + 1) - 1

f(x + 1) = x² + 2x + 1 + 2x + 2 - 1

f(x + 1) = x² + 4x + 2

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Find f(x + 1) - f(x) :
f(x)=x² + 2x - 1 (Given)

f(x + 1 ) = x² + 4x + 2 (found)

f(x + 1) - f(x) = (x² + 4x + 2) - (x² + 2x - 1 )

f(x + 1) - f(x) = x² + 4x + 2 - x² - 2x + 1

f(x + 1) - f(x) = 2x - 3 (verified)

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⭐$\textbf {Cheers}$⭐

Answer 2

I am not sure about this.
answer but I will tried my best.
hope it will helps you........