b. Given f(x) = x - 5 and g(x) = x ^ 2 + 2x - 1 find f(g(x)) and g(f(x)) Expand and simplify your answers. [4 marks]

To find f(g(x)), we substitute the expression for g(x) into f(x): f(g(x)) = f(x^2 + 2x - 1) Now, we substitute the expression for f(x) into the above equation: f(g(x)) = (x^2 + 2x - 1) - 5 Simplifying further: f(g(x)) = x^2 + 2x - 1 - 5 f(g(x)) = x^2 + 2x - 6 Therefore, f(g(x)) = x^2 + 2x - 6. Now, let's find g(f(x)). We substitute the expression for f(x) into g(x): g(f(x)) = g(x - 5) Now, we substitute the expression for g(x) into the above equation: g(f(x)) = (x - 5)^2 + 2(x - 5) - 1 Expanding and simplifying further: g(f(x)) = x^2 - 10x + 25 + 2x - 10 - 1 g(f(x)) = x^2 - 8x + 14 Therefore, g(f(x)) = x^2 - 8x + 14.