Let and defined on the closed interval

MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Let

f(x)=\sqrt{x}

and

g(x)=\tfrac{1}{2}x+k

defined on the closed interval

[0,1]

, where

k

is a real constant. Determine all real values of

k

for which the equation

f(x)=g(x)

has at least one solution in

[0,1]