Multiple Choice Questions circle the appropriate answer Each

Multiple Choice Questions, circle the appropriate answer. Each correct answer gains 2 marks. Let f(x) = 3x - 2 and g(x) = x^2. What is the function f + g ? X^2 + 3x - 2 3x^2 - 2 4x^2 - 2 None of these Let f(x) = -2x - 7 and g(x) = -4x + 3, then evaluate (f o g) (-5). 23 -53 3 Which of the following functions is one-to one? k(x) = x^3 + 2 f(x) = |x| + 3 g(x) = x^4 + 5 None of these Determine x - intercept(s) of y- x^2 + 5x + 6. -2,-3 1,5 2,3 None of these Let f(x) = x/x+16 and g(x) = 18/x+2. What is the domain of function (f. g)(x)? {x| x is any real number} {x| x notequalto 2 and x notequalto 6} {x| x notequalto -2 and x notequalto -6} None of these

Solution

1) f(x) = 3x -2 ; g(x) = x^2

Find f+g : add the two functions: (f +g)(x) = 3x -2 +x^2 = x^2 +3x -2

2) (f o g)(-5)

find (f o g)(x) ; plug x= g(x) in f(x)

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

3) f(x) = -2x -7 ; g(x) = -4x +3

(f o g) (-5)

(f o g)(x) = -2(-4x+3) -7 = 8x -13

(f o g)(-5) = 8(-5) -13 = -53

5) x intercepts of f(x) = x^2 +5x +6

factorise : x^2 +3x +2x +6 =0

x(x+3) +2(x+3) =0

(x+2)(x+3) =0

x= -2 ; x=-3 are x intercepts