Suppose that the function g satisfies g(x) = 2x − 4 for all real numbers x and that g −1 is the inverse function of g. Suppose that the function f satisfies g(f(g −1 (x))) = 2x 2 + 16x + 26 for all real numbers x. What is the value of f(π)?
I got to this step: f ((x + 4)/2) = (x + 4)^2 − 1
In answer key it says
Thus, we can replace (x + 4)/2 with π, which is equivalent to replacing x + 4 with 2π
why can we replace x+4 with 2π?
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As we have to find range for domain pi, but in solution we are getting in terms of x, hence we have to substitue x's value in terms of pi
That is easy!
substuition method, Let (x+4)/2 = pai , so x+4 = 2pai
f (pai) = (2pai)^2-1