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6 problems match “function composition”. Clear

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1. Evaluating a function from its composite form ●○○○○ 10 ptsLet $g(2x + 5) = 4x^2 - 3x + 2$. Find $g(-3)$.
2. Composition of two functions at points ●○○○○ 10 ptsIf $f(x) = x^2-2x+1$ and $g(x) = \sqrt{2x+1}$, what is the value of $f(g(4)) - g(f(3))$?
3. Function value from a shifted definition ●○○○○ 10 ptsIf $f(x+1)=x$ for all real $x$, find $f(6)$.
4. Fixed point of a functional definition ●●○○○ 20 ptsLet $h(4x-1) = 2x + 7$ for all real $x$. For what value of $x$ is $h(x) = x$?
5. Integer point in a composed functional equation ●●●○○ 50 ptsThe function $f(x)$ satisfies $f(f(x)) = 6x - 2005$ for all real numbers $x$. There exists an integer $n$ such that $f(n) = 6n - 2005$. Find $n$.
6. Value of f(2) for a quadratic ●●●○○ 50 ptsLet $a$ and $b$ be real numbers. The quadratic function $f(x)=x^{2}+ax+b$ satisfies $f(f(0))=f(f(1))=0$ and $f(0)\neq f(1)$. Find $f(2)$.