For all values of x f(x) = x^2 + 2 g(x)= x - 5 show that fg(x) = x^2 -10x +27
Firstly, we have to substitute g(x) into the function f(x)So, fg(x) = (g(x))^2 +2
Next we must rewrite the equation on the RHS in terms of x only
So, fg(x) = (x-5)^2 +2
Next we must simplify the RHS by expanding the brackets
So, fg(x) = (x-5)(x-5) +2 = (x^2-10x +25) +2 = x^2 -10x + 27
YS
Related Maths GCSE answers
All answers ▸How do you use the product rule?
The point P has coordinates (3, 4) The point Q has coordinates (a, b) A line perpendicular to PQ is given by the equation 3x + 2y = 7 Find an expression for b in terms of a.
Samuel had 3 piles of coins, I, II and III. Altogether there was 72p. Pile II had twice as much as pile I. Pile III had three times as much as pile II. How much money was in Pile III?
Solve the simultaneous equation 6x + 2y = -3, 4x - 3y =11