Diane B.
asked • 07/05/19Find (g o f)(x). F(x)=x+6, g(x)=x^2-4x+7
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2 Answers By Expert Tutors
Lena K. answered • 07/11/19
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(g o f)(x) translates to g(f(x)) = g(x+6). So we solve:
g(x+6) = (x+6)2 - (x+6) + 7
= x2 + 12x + 36 - x - 6 + 7
= x2 + 11x + 37
Jim L. answered • 07/11/19
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The notation asks for g of f of x. To solve these we replace x in g(x) by f(x) wherever it occurs.
So, ( g o f)(x) = (x+6)^2 -4(x+6) +7
= x^2 + 12x +36 -4x -24 + 7
= x^2 + 8x +19
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Timothy T.
g(x) composed with f(x) = g[f(x)]. Since g(x) = x^2 – 4x +7 and f(x) = x + 6 then replace x in g(x) with x + 6. Now g[f(x)] = (x + 6)^2 – 4(x + 6) + 7. And g[f(x)] = x^2 + 12x + 36 – 4x -24 + 7. Finally g[f(x)] = x^2 + 8x + 19.07/11/19