functions

• If f(x) and g(x) are functions, then g(f(x)) represents the composition of functions.
• f(x) = -3x^3 + 4x
• A linear function has an equation in the form y = mx + b where m is the gradient (steepness) and b is the vertical intercept (y-intercept).
• To find the inverse function of a one-to-one function, swap x and y values in the equation.
• g(x) = x^2 - 5x + 10
• (fog)(x) = (-3)(-5)^3 + 4(-5)
• (fg)(x) = -3(x^2 - 5x + 10)^3 + 4(x^2 - 5x + 10)
• The gradient can be found by taking two points on the line and finding their difference divided by their difference in x values.
• The domain of a function is all possible input values, while its range is all possible output values.
• To find the equation of a straight line given its gradient and one point, substitute the coordinates into the formula y = mx + c to get c as an expression involving only x and y.
• When graphing quadratic equations, it helps to identify any symmetry or axis of symmetry.