検 investigate

FBI agents hide behind a tree to do a risky investigation.

checkup ★★★☆☆
検 (investigate) + 査 (inspect) = 検査 (checkup)

Medical checkup. Also, investigation, inspection, review: (fiancial audit, smog check, check the condition of goods that roll off the assemby line, etc). Has the nuance of a test where something passes or fails.

internet search ★★★☆☆
検 (investigate) + 索 (look up) = 検索 (internet search)

give consideration to ★★☆☆☆ NP
検 (investigate) + 討 (attack/discuss) = 検討 (give consideration to)

to give thorough consideration to the topic. To investigate something thoroughly. Often said by politicians who don't want to give a real answer.