code: def test_apply_options_explicit_backend_persists_other_backend_inverted(
      self,
  ):
      obj = ExampleElement([])
      obj.opts(style_opt1="A", plot_opt1="B", backend="backend_2")
      obj.opts(style_opt1="C", plot_opt1="D", backend="backend_1")
      plot_opts = Store.lookup_options("backend_1", obj, "plot")
      assert plot_opts.options == {"plot_opt1": "D"}
      style_opts = Store.lookup_options("backend_1", obj, "style")
      assert style_opts.options == {"style_opt1": "C"}
      plot_opts = Store.lookup_options("backend_2", obj, "plot")
      assert plot_opts.options == {"plot_opt1": "B"}
      style_opts = Store.lookup_options("backend_2", obj, "style")
      assert style_opts.options == {"style_opt1": "A"}
  
imports: import gc
  from holoviews.core.element import Element
  from holoviews.core.options import Keywords, Options, OptionTree, Store
  from holoviews.core.spaces import HoloMap
  from ..utils import LoggingComparisonTestCase
label_desc: Use image node_id 20 for calling the TestDimensioned_options obj's underlying member method code with example usage: obj.test_apply_options_explicit_backend_persists_other_backend_inverted() without return types