SOLUTION: given f =x-4 and g=x^2+3 , show that gf(x) = x^2- 8x + 19 hence find the values of x for which gf (x) = 4

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Question 762704: given f =x-4 and g=x^2+3 , show that gf(x) = x^2- 8x + 19
hence find the values of x for which gf (x) = 4
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = x - 4
g(x) = x^2 + 3
g(f(x)) = g(x - 4) = (x-4)^2 + 3 = x^2 - 8x + 16 + 3 = x^2 - 8x + 19
g(f(x)) = 4 means that x^2 - 8x + 19 = 4 or
x%5E2+-+8%2Ax+%2B+15+=+0
Using factorizing to solve the quadratic
%28x+-+5%29%2A%28x+-+3%29+=+0
x = 5 or x = 3 are the possible solutions.
:)