What supply voltage(s) do you have?
How much current does the 1.5V to 7.5V output have to supply?
An opamp can do it with good linearity and accuracy, however, the stability of the DC offset is only as good as the opamp's voltage reference. If that reference is created by a voltage divider from the opamp's power supply, then any variation of the offset goes directly to the opamp output. If this is critical, then use a voltage reference IC to create the required offset at the input of the opamp.