If f(x) = 3x^2 and g(x) = x - 3, when is gof(x) = fog(x)

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The function f(x) = 3x^2 and g(x) = x - 3.

fog(x) = f(g(x)) = f(x - 3) = 3*(x -3)^2

gof(x) = g(f(x)) = g(3x^2) = 3x^2 - 3

gof(x) = fog(x)

=> 3*(x -3)^2 = 3x^2 - 3

=> (x - 3)^2 = x^2 - 1

=> x^2 - 6x + 9 = x^2 - 1

=> 6x = 10

=> x = 5/3

The value of fog(x) = gof(x) when x = 5/3

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tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

The functions f(x) and g(x) are defined as f(x) = 3x^2 and g(x) = x - 3.

gof(x) = g(f(x))

= g(3x^2)

= 3x^2 - 3

fog(x) = f(g(x))

= f(x - 3)

= 3*(x - 3)^2

If gof(x) =fog(x)

3x^2 - 3 = 3*(x - 3)^2

x^2 - 1 = x^2 + 9 - 6x

6x = 10

x = 5/3

At x = 5/3, fog(x) = gof(x)

, when is gof(x) = fog(x)

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