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Let f(x) = 9x^2 − x 1. Find the following f(x − 1) f(x 1) and f(x 2h)

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Part (a): For the expression f(x - 1) + f(x + 1) = 18x^2 + 20. Part (b): For the expression f(x + 2h) = 9x^2 + 35hx + 36h^2 - 2h + 1.

Let's find the following for the function f(x) = 9x^2 – x + 1:

(a) f(x - 1) + f(x + 1)

(b) f(x + 2h)

Steps to solve:

Part (a):

Distribute the terms:

f(x - 1) + f(x + 1) = 9(x - 1)^2 - (x - 1) + 9(x + 1)^2 + (x + 1)

Expand the squares:

f(x - 1) + f(x + 1) = 9(x^2 - 2x + 1) - x + 1 + 9(x^2 + 2x + 1) + x + 1

Combine like terms:

f(x - 1) + f(x + 1) = 18x^2 + 18 + 2

Simplify:

f(x - 1) + f(x + 1) = 18x^2 + 20

Part (b):

Substitute x + 2h into the function:

f(x + 2h) = 9(x + 2h)^2 - (x + 2h) + 1

Expand the square:

f(x + 2h) = 9(x^2 + 4hx + 4h^2) - x - 2h + 1

Distribute the terms:

f(x + 2h) = 9x^2 + 36hx + 36h^2 - x - 2h + 1

Combine like terms:

f(x + 2h) = 9x^2 + 35hx + 36h^2 - 2h + 1

Complete question:

Let f(x) = 9x^2 – x + 1. Find the following. = (a) f(x - 1) + f(x + 1) (b) f(x + 2h)

User Ylisar
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