Chapter 5 - Algebra Coach Exercises



Algebra Coach Exercise on substituting expressions into functions.
Each question contains two formulas. The second formula defines a function called f with argument x. The first formula gives an expression to substitute in for x. Drag-and-drop each of these problems into the Algebra Coach and click the Substitute button to carry out the substitution.
  1. x = 5,   f (x) = x^3 + 10 x +2
  2. x = a,   f (x) = sqrt (5 - x^2)
  3. x = x + 2,   f (x) = sqrt (5 - x^2)
  4. x = x + h,   f (x) = 1 / sqrt (5 - x^2)


Algebra Coach Exercise on composition of functions.
Each question below contains two formulas. The first formula defines a function y = f (x) and the second formula defines a function z = g (y). Substituting the first function, f, into the second function, g, produces the composite function , like this:
To do this in the Algebra Coach drag-and-drop each of these problems into the Algebra Coach and click the Substitute button.
  1. y = x + 3,   z = y^2 - 2 y
  2. y = x^2 - 2 x,   z = y + 3
  3. y = x + 2,   z = sqrt (5 - y^2)
  4. y = x + h,   z = 1 / sqrt (5 - y^2)


Algebra Coach Exercise on the inverse of a function.
Each question below contains two formulas. The first formula defines a function y = f (x) and the second formula defines a function z = g (y). Substituting the first function, f, into the second function, g, produces the composite function , like this:
We claim that g is the inverse function of f. If this is true then the composite function should have no overall effect and we should find that z = x (the output should equal the input). To check this claim in the Algebra Coach drag-and-drop each of these problems into the Algebra Coach and click the Substitute button. Then click on the Do to right side button and then on the Simplify button repeatedly.
  1. y = 3 x,   z = y / 3
  2. y = 2 x + 3,   z = (y - 3) / 2
  3. y = -2 x + 3,   z = (-y + 3) / 2
  4. y = 5 / 9 (x - 32),   z = 9 y / 5 + 32
  5. y = (arcsin(x) - 4)/3,   z = sin(3y + 4)
  6. y = log(x/3),   z = 3 * 10^y