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If f(x) = x² - 6x, find: f(a+1) -f(a) = I know the answer is 2a-5 but I don't understand how we get the answer. Mainly how we get 2a from (a+1)² - 6(a+1) - (a²-6a). Please show work and explain how we get the 2a.

Respuesta :

[tex]f(x) = x^2 - 6x\\\\f(a) = a^2 - 6a\\\\f(a+1) = (a+1)^2 - 6(a+1)\\\\f(a+1) = a^2+2a+1 - 6a-6\\\\f(a+1) = a^2-4a-5\\\\[/tex]

Then,

[tex]f(a+1)-f(a) = (a^2-4a-5) - (a^2-6a)\\\\f(a+1)-f(a) = a^2-4a-5 - a^2+6a\\\\f(a+1)-f(a) = (a^2-a^2)+(-4a+6a)-5\\\\f(a+1)-f(a) = 2a-5\\\\[/tex]

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