Algebra 2
If f(x)= x^2 + 3 and g(x) = 3x - 1 then find the following:
1a. (f+g)(x)
1b. (f+g)(3)
1c. (f-g)(x)
1d. (fg)(x)
1e. (fg)(-1)
1f. (f/g)(x)
1g. (f o g)(x)
1h. (f o g)(1)
1i. (g o f)(x)
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Answers
1a. (f+g)(x) = x^2 + 3 + 3x - 1 = x^2 + 3x + 2 1b. (f+g)(3) = 3^2 + 3x + 2 = 12 1c. (f-g)(x) = x^2 + 3 - 3x + 1 = x^2 - 2x + 4 1d. (fg)(x) = (x^2 + 3)(3x - 1) = 3x^3 + 9x - (x^2 + 3) 1e. (fg)(-1) = 3(-1)^3 + 9(-1) - (-1^2 + 3) = -3 - 9 - (-2 + 3) = -3 - 6 - (-2) = -11 1f. (f/g)(x) = (x^2 + 3)/(3x - 1), not defined for x = 1/3 1g. (f o g)(x) = f(g(x)) = f(3x - 1) = (3x - 1)^2 + 3 = 9x^2 - 6x + 4 1h. (f o g)(1) = (1)^2 + 3 = 4 1i. (
