Solve the following questions: a) If h(x) = bx - 5 and h(4) = -1, find b. b) Simplify g(x) = (x2 - 1)/(x - 1). c) State the domain of definition of g(x).

Hey senobiashanyuy, good to see you again. Here's the solution for question 6: a) Step 1: Substitute x=4 into the function h(x) = bx - 5. h(4) = b(4) - 5 Step 2: Use the given information that h(4) = -1 to set up an equation. 4b - 5 = -1 Step 3: Add 5 to both sides of the equation. 4b = -1 + 5 4b = 4 Step 4: Divide by 4 to solve for b. b = (4)/(4) b = 1 The value of b is 1. b) Step 1: Factor the numerator x^2 - 1 using the difference of squares formula, a^2 - b^2 = (a-b)(a+b). x^2 - 1 = (x-1)(x+1) Step 2: Substitute the factored numerator back into the expression for g(x). g(x) = ((x-1)(x+1))/(x-1) Step 3: Cancel out the common term (x-1) from the numerator and the denominator. g(x) = x+1 The simplified expression for g(x) is x+1. c) Step 1: Identify any values of x that would make the denominator of the original function g(x) = (x^2 - 1)/(x - 1) equal to zero. The denominator is x-1. x-1 = 0 x = 1 Step 2: The domain of definition includes all real numbers except for the values that make the denominator zero. Therefore, x ≠ 1. The domain of definition of g(x) is all real numbers except x=1. Send me the next one 📸