Roku remotes cannot directly control the tv's input/source control. BUT, the tv itself may do this for you if it supports the CEC feature. Unfortunately many tv manufacturers call this feature by their own proprietary names. Some common ones:
• AOC: E-link
• Hitachi: HDMI-CEC
• LG: SimpLink or SIMPLINK (HDMI-CEC)
• Mitsubishi: NetCommand for HDMI, Realink for HDMI
• Panasonic: VIERA Link, HDAVI Control, EZ-Sync
• Onkyo: RIHD (Remote Interactive over HDMI)
• Philips: EasyLink
• Pioneer: Kuro Link
• Runco International: RuncoLink
• Samsung: Anynet+
• Sharp: Aquos Link
• Sony: BRAVIA Link, BRAVIA Sync, Control for HDMI
• Toshiba: CE-Link, Regza Link
Some other names shared by multiple manufacturers:
• Fun-Link, INlink, T-Link
On some TVs you may need to have the TV do a scan or search for connected CEC devices, some do it automatically when they start up.
To turn this feature on in your Roku, enable "1-touch play" via Roku menu path "Settings > System > Control other devices".
Maybe I'm lucky but I'm not experiencing the problems Jim has with my 10+ year old Samsung. I press a Roku control key on the Roku remote (not the volume, mute, or power keys which act on the tv not the Roku) and the Roku sends the appropriate CEC commands over the HDMI connection so that my Samsung turns on if necessary, then switches to the Roku's HDMI input.
Note: If other connected devices (game console, cable box, disk player, etc) also have a CEC function, pressing a button on the their remotes may also switch the tv to their tv inputs.