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
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