public abstract double transform(double x);

  /**
   * Returns the inverse linear transformation. The inverse of a horizontal transformation is a
   * vertical transformation, and vice versa. The inverse of the {@link #forNaN} transformation is
   * itself. In all other cases, the inverse is a transformation such that applying both the
   * original transformation and its inverse to a value gives you the original value give-or-take

  }

  AbstractBiMap<V, K> makeInverse(Map<V, K> backward) {
    return new Inverse<>(backward, this);
  }

  void setInverse(AbstractBiMap<V, K> inverse) {
    this.inverse = inverse;
  }

  // Query Operations (optimizations)

  @Override
  public boolean containsValue(@Nullable Object value) {
    return inverse.containsKey(value);
  }

  // Modification Operations

    assertFalse(getMap().containsKey(k0()));

    assertTrue(getMap().containsKey(k1()));
    assertTrue(getMap().inverse().containsKey(null));
    assertNull(getMap().get(k1()));
    assertEquals(k1(), getMap().inverse().get(null));
    assertEquals(1, getMap().size());
  }

  // nb: inverse is run through its own entire suite

  @MapFeature.Require(SUPPORTS_PUT)
  @CollectionSize.Require(ZERO)

      Entry<V, K> reversed = reverseEntry(entry);
      BiMap<V, K> inv = getMap().inverse();
      assertFalse(
          "Inverse should not contain entry " + reversed, inv.entrySet().contains(reversed));
      assertFalse(
          "Inverse should not contain key " + reversed.getKey(),
          inv.containsKey(reversed.getKey()));
      assertFalse(
          "Inverse should not contain value " + reversed.getValue(),

    }
    ImmutableMap<V, K> backwardMap = builder.build();
    this.inverse = new RegularImmutableBiMap<V, K>(backwardMap, this);
  }

  RegularImmutableBiMap(ImmutableMap<K, V> delegate, ImmutableBiMap<V, K> inverse) {
    super(delegate);
    this.inverse = inverse;
  }

  @Override
  public ImmutableBiMap<V, K> inverse() {
    return inverse;
  }

    this.singleKey = singleKey;
    this.singleValue = singleValue;
    this.inverse = null;
  }

  private SingletonImmutableBiMap(K singleKey, V singleValue, ImmutableBiMap<V, K> inverse) {
    this.singleKey = singleKey;
    this.singleValue = singleValue;
    this.inverse = inverse;
  }

  @Override
  public @Nullable V get(@Nullable Object key) {

    this.singleValue = value;
    this.inverse = inverse;
  }

  @Override
  public ImmutableBiMap<V, K> inverse() {
    ImmutableBiMap<V, K> result = inverse;
    if (result == null) {
      return inverse = new SingletonImmutableBiMap<V, K>(singleValue, singleKey, this);
    } else {
      return result;
    }
  }

  @Override
  public ImmutableSet<V> values() {
    return ImmutableSet.of(singleValue);
  }

    assertFalse(getMap().containsKey(k0()));

    assertTrue(getMap().containsKey(k1()));
    assertTrue(getMap().inverse().containsKey(null));
    assertNull(getMap().get(k1()));
    assertEquals(k1(), getMap().inverse().get(null));
    assertEquals(1, getMap().size());
  }

  // nb: inverse is run through its own entire suite

  @MapFeature.Require(SUPPORTS_PUT)
  @CollectionSize.Require(ZERO)

      Entry<V, K> reversed = reverseEntry(entry);
      BiMap<V, K> inv = getMap().inverse();
      assertFalse(
          "Inverse should not contain entry " + reversed, inv.entrySet().contains(reversed));
      assertFalse(
          "Inverse should not contain key " + reversed.getKey(),
          inv.containsKey(reversed.getKey()));
      assertFalse(
          "Inverse should not contain value " + reversed.getValue(),

      @Nullable JdkBackedImmutableBiMap<V, K> inverse) {
    this.entries = entries;
    this.forwardDelegate = forwardDelegate;
    this.backwardDelegate = backwardDelegate;
    this.inverse = inverse;
  }

  @Override
  public int size() {
    return entries.size();
  }

  @Override
  public ImmutableBiMap<V, K> inverse() {
    return inverse != null ? inverse : lazyInverse();
  }