Write the equation of the function g (x) if g (x) = f (x+2) + 4 and f (x) = x^3 - 7

Question

Mathematics

Maximo French

23 July, 20:04

Write the equation of the function g (x) if g (x) = f (x+2) + 4 and f (x) = x^3 - 7

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Dillon Santos · Answer 1

F (x) = x³ - 7

f (x + 2) = (x + 2) ³ - 7

f (x + 2) = (x + 2) (x + 2) (x + 2) - 7

f (x + 2) = (x (x + 2) + 2 (x + 2)) (x + 2) - 7

f (x + 2) = (x (x) + x (2) + 2 (x) + 2 (2)) (x + 2) - 7

f (x + 2) = (x² + 2x + 2x + 4) (x + 2) - 7

f (x + 2) = (x² + 4x + 4) (x + 2) - 7

f (x + 2) = (x² (x + 2) + 4x (x + 2) + 4 (x + 2)) - 7

f (x + 2) = (x² (x) + x² (2) + 4x (x) + 4x (2) + 4 (x) + 4 (2)) - 7

f (x + 2) = (x³ + 2x² + 4x² + 8x + 4x + 8) - 7

f (x + 2) = (x³ + 6x² + 12x + 8) - 7

f (x + 2) = x³ + 6x² + 12x + 8 - 7

f (x + 2) = x³ + 6x² + 12x + 1

g (x) = f (x + 2) + 4

g (x) = (x³ + 6x² + 12x + 1) + 4

g (x) = x³ + 6x² + 12x + 1 + 4

g (x) = x³ + 6x² + 12x + 5