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Maths Functions Question?
When f(x)=x^2 and g(x)=2x+3 with f and g defined on a suitable domain, if f(g(k))=49 then find the values of k.
1 Answer
- ?Lv 79 years agoFavorite Answer
f(g(k)) = f(2k + 3) by definition of g(x); f(2k + 3) = (2k + 3)^2 by definition of f(x) ; so (2k+3)^2 = 49;
Normally we would expand the bracket, simplify the resulting Quadratic Equation etc., but there is an easier way - just take the square root of each side i.e. if (2k+3)^2 = 49, 2k+3 = =/-7
So 2k+3 = 7 or 2k+3 = -7, so 2k = 4 or -10, so k = 2 or -5.
Source(s): Retired Maths Teacher
