(a) If g(x) = 3x + 2 and h(x) = 9x2 + 12x + 9, find a function f such
that f o g = h. (Think about what operations you would have to perform on the formula for g to end up with the formula for h.)
f = 1
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(b) If f(x) = 3x + 9 and h(x) = 3x2 + 3x + 6, find a function g such
that f o g = h.
g(x) = 2
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how would i do such a question??
no formal steps ... I just played with the given functions.
for instance ...
f(3x+2) = 9x^2 + 12x + 9
if (3x+2) is squared, you get 9x^2 + 12x + 4
note that you are short 5 units of the constant value. so ...
f(x) = x^2 + 5
for the second ...
f[g(x)] = 3[g(x)] + 9 = 3x^2 + 3x + 6
note that h(x) has coefficients of 3 for the first two terms ...
so I tried 3(x^2 + x) + 9 = 3x^2 + 3x + 9
but, the constant is 6 ... I have 3 units too many. How can I get rid of the additional 3 ?
3(x^2 + x - 1) + 9 = 3x^2 + 3x - 3 + 9 = 3x^2 + 3x + 6