Question

For all values of x, f(x) = x^2 + 1 and g(x) = x-5

(a) Show that fg(x) = x^2 - 10x + 26
(b) Solve fg(x) = gf(x)

Answer 1

a) f g(x) = x³ - 5 x² + x -5

b) g(f(x) = x³ - 5 x² + x -5

Explanation:

Step(i):-

Given that f(x) = x² + 1 and g(x) = x-5

a)

f(g(x)) = f(x-5) = (x-5)²+1 = x² - 10x +25 +1 = x² - 10 x +26

Step(ii):-

a) f g(x) = f(x) g(x) = (x² + 1 )(x-5) = x³ - 5 x² + x -5

b) g(f(x) = g(x) f(x) = (x-5) (x²+1) = x³ - 5 x² + x -5