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simulate this circuit – Schematic created using CircuitLab
The feedback network I am using is a voltage divider with 4.7K and a 1K resistor. The node after the 4.7K resistor is connected to the inverting input of the amp. The node after the 1K is grounded. Attached is the hyperlink to the LF351 datasheet.
LF351 doesn't have rail-to-rail input capability, not even close.
With +/- 15 V supplies, the minimum common mode input voltage is specified as -11 V, with typical operation to -12 V. Translated to your +10.5/-0V supplies, this means you need to keep the input common mode voltage above 3 V (if you want to fuss around and take a risk) or 4 V (to be sure it will work).
You should either use a wider supply range (+/- 12 or +/- 15 V) or choose an op-amp better suited to the supplies you have.
The LF351 uses FETs are may be biased up to V+ but not within 3V above V-=0V
So your biasing to 0V is incorrect.
Suggestion:
Better: Define your input and output range and thus define gain with offset specs.
You may consider an Op Amp that can sense near 0V or bias both inputs to V+/2
I have never seen an old LF351 but a TL081 is similar and has the "Opamp Phase Inversion" problem where the output saturates as high as it can go when an input has a voltage within 3V or 4V from the ground voltage in your circuit.
