For a real parameter

MATHEMATICS · Subjective · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

k

, let

f_k(x)= \begin{cases} x^{2}-k, & 0\le x\le 2\\[4pt] k\ln x, & 2< x\le 4 \end{cases}

Find all real values of

k

for which the equation

f_k(x)=0

has at least one solution in

[0,4]