Final answer:
The Texas Appraiser Licensing and Certification Board (TALCB) is the entity granted authority to adopt rules for the approval of appraiser trainees under the Texas appraiser licensing law.
Step-by-step explanation:
Under the Texas appraiser licensing law, the authority to adopt rules for the approval of appraiser trainees was given to the Texas Appraiser Licensing and Certification Board (TALCB). This board is responsible for regulating the process of appraising real property in the state of Texas, which includes setting the standards for licensing appraisers and appraiser trainees. While there are other state officials and commissions, such as the commissioner of the Department of Agriculture and the three commissioners of the Railroad Commission, their regulatory jurisdictions cover different areas, such as agriculture, certain public utilities, transportation, and the oil and gas industry, rather than the appraisal industry.