An $n$ -Fold Shrinking Function

★ 7/10functions Quadratic Equations Substitution Logarithms

Problem

Let $f(x)$ have domain $D$ . If there exists $[a, b] \subseteq D$ such that the minimum of $f(x)$ on $[a, b]$ is $\dfrac{a}{n}$ and the maximum is $\dfrac{b}{n}$ , where $n$ is a positive integer, then $f(x)$ is called an $n$ -fold shrinking function. If

f(x) = \log_4\left(2^x + t\right)

is a $4$ -fold shrinking function, find the range of possible values of the real number $t$ .

Answer

Solution

Difficulty	7/10
Topics	functions, Quadratic Equations, Substitution, Logarithms

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