標題:
S4 Maths ( f(x) )
4. Consider the function f(x) = (x-3)(x+1)-(x-2)(x+2)a) Determine the type of function f(x).b) Find the x-intercept(s) and y-intercept of the graph of y=f(x).9.It is given that g(x) = a(x-1)(x+1) - b(x +1)^2 ,g(1) = 4 and g(0) = -3a) Find the values of a and b.b) Factorize g(x).c) Hence,... 顯示更多 4. Consider the function f(x) = (x-3)(x+1)-(x-2)(x+2) a) Determine the type of function f(x). b) Find the x-intercept(s) and y-intercept of the graph of y=f(x). 9.It is given that g(x) = a(x-1)(x+1) - b(x +1)^2 ,g(1) = 4 and g(0) = -3 a) Find the values of a and b. b) Factorize g(x). c) Hence, solve g(x) = 0.
最佳解答:
4a)f(x) = (x - 3)(x + 1) - (x - 2)(x + 2) = (x2 - 2x - 3) - (x2 - 4) = - 2x + 1. ∴ f(x) is a linear function. b)y = f(x) y = - 2x + 1 2x + y = 1 x / (1/2) + y / (1) = 1 ............. (Intercept form : x/a + y/b = 1) ∴ x - intercept = 1/2 , y - intercept = 1. 9a) g(x) = a(x - 1)(x + 1) - b(x + 1)2g(1) = 4 a(1 - 1)(1 + 1) - b(1 + 1)2 = 4 0 - 4b = 4 b = - 1g(0) = - 3 a(0 - 1)(0 + 1) - b(0 + 1)2 = - 3 - a - b = - 3 - a - (-1) = - 3 a = 4 b)Substitute a = 4 and b = - 1 into g(x) :g(x) = 4(x - 1)(x + 1) - (- 1)(x + 1)2 g(x) = (x + 1) [ 4(x - 1) + (x + 1) ] g(x) = (x + 1) (5x - 3) c)g(x) = 0 (x + 1) (5x - 3) = 0 x + 1 = 0 or 5x - 3 = 0 x = - 1 or x = 3/5
其他解答:
S4 Maths ( f(x) )
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發問:4. Consider the function f(x) = (x-3)(x+1)-(x-2)(x+2)a) Determine the type of function f(x).b) Find the x-intercept(s) and y-intercept of the graph of y=f(x).9.It is given that g(x) = a(x-1)(x+1) - b(x +1)^2 ,g(1) = 4 and g(0) = -3a) Find the values of a and b.b) Factorize g(x).c) Hence,... 顯示更多 4. Consider the function f(x) = (x-3)(x+1)-(x-2)(x+2) a) Determine the type of function f(x). b) Find the x-intercept(s) and y-intercept of the graph of y=f(x). 9.It is given that g(x) = a(x-1)(x+1) - b(x +1)^2 ,g(1) = 4 and g(0) = -3 a) Find the values of a and b. b) Factorize g(x). c) Hence, solve g(x) = 0.
最佳解答:
4a)f(x) = (x - 3)(x + 1) - (x - 2)(x + 2) = (x2 - 2x - 3) - (x2 - 4) = - 2x + 1. ∴ f(x) is a linear function. b)y = f(x) y = - 2x + 1 2x + y = 1 x / (1/2) + y / (1) = 1 ............. (Intercept form : x/a + y/b = 1) ∴ x - intercept = 1/2 , y - intercept = 1. 9a) g(x) = a(x - 1)(x + 1) - b(x + 1)2g(1) = 4 a(1 - 1)(1 + 1) - b(1 + 1)2 = 4 0 - 4b = 4 b = - 1g(0) = - 3 a(0 - 1)(0 + 1) - b(0 + 1)2 = - 3 - a - b = - 3 - a - (-1) = - 3 a = 4 b)Substitute a = 4 and b = - 1 into g(x) :g(x) = 4(x - 1)(x + 1) - (- 1)(x + 1)2 g(x) = (x + 1) [ 4(x - 1) + (x + 1) ] g(x) = (x + 1) (5x - 3) c)g(x) = 0 (x + 1) (5x - 3) = 0 x + 1 = 0 or 5x - 3 = 0 x = - 1 or x = 3/5
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