If f(x) = 3x^2 - x + 2, find f(2), f(-2), f(a), f(-a), f(a+1), 2*f(a), f(2a), f(a^2), (f(a))^2 and f(a+h)

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The function f(x) = 3x^2 - x + 2. To determine the value of f(x) for different values of x, substitute for x in the expression of the function and simplify.

f(2) =3*(2)^2 - 2 + 2

= 3*8

= 24

f(-2) = 3*(-2)^2 - (-2) + 2

= 3*8 + 2 + 2

= 24 + 4

 = 28

f(a) = 3a^2 - a + 2

f(-a) = 3a^2 + a + 2

f(a+1) = 3(a+1)^2 + (a + 1) + 2

= 3*(a^2 + 2a + 1) + a + 1 + 2

=3a^2 + 6a + 3 + a + 3

= 3a^2 + 7a + 6

2*f(a) = 3*(3a^2 - a + 2)

= 6a^2 - 3a + 6

f(2a) = 3*(2a)^2 - 2a + 2

= 3*4a^2 - 2a + 2

= 12a^2 - 2a + 2

f(a^2) = 3*(a^2)^2 - a^2 + 2

= 3a^4 - a^2 + 2

(f(a))^2 = (3a^2 - a + 2)^2

f(a+h) = 3(a+h)^2 - (a+h) + 2

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