Given the functions f(x) = x2, g(x) = rac1x-4, and h(x) = kx+m. a) Explain the meaning of x eq 4 in g(x). b) Find g(0). c) Find g^-1(0). d) Find k and m if f ext o h(x) = 9x2 - 12x + 4.

Here are the solutions for questions 1 and 3. Question 1: Given the functions f(x) = x^2, g(x) = (1)/(x-4), and h(x) = kx+m. a) Explain the meaning of the statement "x ≠ 4" in the function g(x). The statement x ≠ 4 means that x can be any real number except 4. If x were equal to 4, the denominator of g(x) would become zero, making the function undefined. b) Find g(0). Step 1: Substitute x=0 into the function g(x). g(0) = (1)/(0-4) Step 2: Simplify the expression. g(0) = (1)/(-4) = -(1)/(4) The value of g(0) is -(1)/(4). c) Find g^-1(0). Step 1: Find the inverse function g^-1(x). Let y = g(x) = (1)/(x-4). Swap x and y: x = (1)/(y-4) Step 2: Solve for y. x(y-4) = 1 y-4 = (1)/(x) y = (1)/(x) + 4 So, g^-1(x) = (1)/(x) + 4. Step 3: Substitute x=0 into g^-1(x). g^-1(0) = (1)/(0) + 4 Division by zero is undefined. The value of g^-1(0) is undefined. d) The value of k and m given that f h(x) = 9x^2 - 12x + 4. Step 1: Find the composite function f h(x). f h(x) = f(h(x)) = f(kx+m) Substitute h(x) into f(x): f(kx+m) = (kx+m)^2 Step 2: Expand the expression. (kx+m)^2 = k^2x^2 + 2kmx + m^2 Step 3: Equate this to the given expression 9x^2 - 12x + 4. k^2x^2 + 2kmx + m^2 = 9x^2 - 12x + 4 Step 4: Compare the coefficients of x^2, x, and the constant terms. From the coefficient of x^2: k^2 = 9 k = ± 3 From the constant term: m^2 = 4 m = ± 2 From the coefficient of x: 2km = -12 Step 5: Determine the correct pairs of k and m. If k=3: 2(3)m = -12 6m = -