f(x-1)-f(x)=[3(x-1)-9]-[3x-9]

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Solution for f(x-1)-f(x)=[3(x-1)-9]-[3x-9] equation:


Simplifying
f(x + -1) + -1f(x) = [3(x + -1) + -9] + -1[3x + -9]

Reorder the terms:
f(-1 + x) + -1f(x) = [3(x + -1) + -9] + -1[3x + -9]
(-1 * f + x * f) + -1f(x) = [3(x + -1) + -9] + -1[3x + -9]
(-1f + fx) + -1f(x) = [3(x + -1) + -9] + -1[3x + -9]

Multiply f * x
-1f + fx + -1fx = [3(x + -1) + -9] + -1[3x + -9]

Combine like terms: fx + -1fx = 0
-1f + 0 = [3(x + -1) + -9] + -1[3x + -9]
-1f = [3(x + -1) + -9] + -1[3x + -9]

Reorder the terms:
-1f = [3(-1 + x) + -9] + -1[3x + -9]
-1f = [(-1 * 3 + x * 3) + -9] + -1[3x + -9]
-1f = [(-3 + 3x) + -9] + -1[3x + -9]

Reorder the terms:
-1f = [-3 + -9 + 3x] + -1[3x + -9]

Combine like terms: -3 + -9 = -12
-1f = [-12 + 3x] + -1[3x + -9]

Remove brackets around [-12 + 3x]
-1f = -12 + 3x + -1[3x + -9]

Reorder the terms:
-1f = -12 + 3x + -1[-9 + 3x]
-1f = -12 + 3x + [-9 * -1 + 3x * -1]
-1f = -12 + 3x + [9 + -3x]

Reorder the terms:
-1f = -12 + 9 + 3x + -3x

Combine like terms: -12 + 9 = -3
-1f = -3 + 3x + -3x

Combine like terms: 3x + -3x = 0
-1f = -3 + 0
-1f = -3

Solving
-1f = -3

Solving for variable 'f'.

Move all terms containing f to the left, all other terms to the right.

Divide each side by '-1'.
f = 3

Simplifying
f = 3

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