Question

Determine
f(a + h) - f(a)
for f(x) = 1 - x2 and simplify.

Answer 1

Answer:

h^2+2ah

Step-by-step explanation:

When f(x) = 1-x^2

f(a) = 1 - a^2

f(a+h) = 1 - (a+h)^2

= 1 - a^2 + 2ah + h^2

Subtracting the two:

f(a+h) - f(a)

= (1 - a^2 + 2ah + h^2) - (1-a^2)

= 1 - 1 - a^2 + a^2 + 2ah + h^2

= 2ah + h^2

= h^2 + 2ah

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